Babbage’s Difference Engine

Thursday, February 17, 2005

HISTORY OF BABBAGE’S DIFFERENCE ENGINE No. 1

HISTORY OF BABBAGE’S DIFFERENCE ENGINE No. 1 BY C.J.D. ROBERTS M.A. Phase I (1821- May 1829) Late in 1820 the Astronomical Society of London commissioned on behalf of its members the production of an accurate set of tables of all the Greenwich stars, tables to reduce the observed positions of these stars to their true positions.

The ones that had been produced officially by the Royal Observatory were not reliable enough and were full of errors. As had always been the case such tables had to be calculated manually. To minimise flaws in the process the method used was to set two human computers first to work out each page independently and then to compare their figures afterwards. Members of the Society were asked to undertake the validation of the results.

During the summer of 1821 Charles Babbage and his friend, John Herschel, the famous astronomer checking over the work of two such human computers, when one remarked to the other because of the number of mistakes they had found:- “I wish to God these tables had been calculated by steam!” Babbage replied that he thought that that was quite possible.

That Summer the two of them went on a six week tour together to the Alps. They probably spent much of their time discussing possibilities. In the autumn, after they had returned, Babbage set forth to fulfil this wish.

In semi-seclusion he worked for several months on the plans of an automatic calculating engine, letting only the Herschels and one or two other friends into his secret. He based it on the mathematical Method of Differences.

He chose this algorithm for two reasons

(1) because of the extensive and comprehensive range of mathematical tables which could be generated by using it, and

(2) because of the simplicity of the arithmetical operation required to perform it, addition, the latter which could easily be translated into machinery.

After two or three trial designs for the engine on paper, he arranged for a small experimental model to be constructed. This was ready to show to his friends and colleagues by May 1822.

By June that year he was ready to announce to the world his invention of the Difference Engine with a short entry in the Astronomical Society’s Journal. Some of his friends were sceptical of the experimental model’s performance, seeing little purpose in the contrivance.

Most, however, were impressed by it, especially with its speed and accuracy when compared with the rate at which humans could carry out the same calculations. In particular it captured the imagination of Sir Humphry Davy, the then President of the Royal Society.

Babbage convinced him that it was not only a calculating machine, but that, as he had also designed a means whereby its results could automatically be printed, accurate mathematical tables could thus be produced as cheap as potatoes.

Davy invited him to draft an open letter to him on the subject. This Babbage did by July of that year, arranging for it to be printed and circulating many copies of it amongst his friends and colleagues as well as Fellows of the Royal Society.

Babbage used this opportunity to outline the national importance of his invention. He explained how during the recent French Revolution that their Government had invested a huge sum of money in the manual calculation of a large set of mathematical tables under the direction of Gasparde Riche de Prony, who had prepared them also by using the Method of Differences.

These the French Government had wanted to arrange to be printed, a project that, after the Napoleonic wars, had also interested the British Government.

Babbage went on to say that a larger version of his engine could do the same job better, not only saving the labour of the large number of people used when constructing such tables, but one which would produce them fully automatically with all errors in them eliminated.

That as his machine was based on the method of differences it could also calculate almost any kind of table: astronomical and naval as well as mathematical; a veritable machine for manufacturing tables.

It is significant, however that he added in the same letter this proviso:- “Whether I shall construct a larger engine of this kind, and bring to perfection the others I have described, will in a great measure depend on the nature of the encouragement I may receive.” He also sent copies of this letter to several popular scientific journals, some of whom reprinted extracts from it.

These had a large circulation and as a result his proposal received considerable publicity. It was perhaps inevitable that it would sooner or later come to the attention of the British Government.

This indeed took place, mainly through the agency of Davies Gilbert, who happened to be both a Member of Parliament as well as a Fellow of the Royal Society. (It is interesting to note that Sir Humphry Davy had been Gilbert’s protegé during his early career.)

Gilbert secured the backing of a large body in Parliament for the project. In the meantime Babbage’s friend, John Herschel, who had become a member of the Board of Longitude, had brought it to their attention as well. In this manner and after much lobbying by his friends, Babbage gained the interest of several politicians in his project. In March 1823, at one of its regular meetings, the Board of the Treasury asked the Royal Society to consider the merits and utility of Babbage’s proposal.

On May 1st they submitted a favourable reply. As a consequence Babbage’s letter to Sir Humphry Davy received formal acknowledgement by being published as a Parliamentary Paper. At the same time another close friend of Babbage’s, Sir Edward Ffrench Bromhead, had proposed to the Astronomical Society that Babbage should be awarded with their gold medal for his invention.

This they elected to do. This was very timely, for the Chancellor of the Exchequer, Robinson, had, in fact, decided to kill the project, as the Government at that time was short of money. However, as the Astronomical Society had decided to honour Babbage with their medal, following the personal intervention of William Brougham, and a private interview with Babbage himself, the Chancellor changed his mind. During this interview Babbage persuaded Robinson that, unlike other inventions, where it might be expected that the inventor could be rewarded for his efforts through the marketing of the produce of his innovation, one could not hope this one to make a profit for its contriver.

But rather, because of its very apparent importance to a nation dependent on a large navy, it was therefore a suitable project for the Government to sponsor. In consequence Robinson agreed to allocate £1500 out of the Civil Contingency Fund to commence the project, a source of funds over which he had personal control without the need for the direct approval of Parliament, which might delay its start. In August 1823 Babbage received the warrant of the Treasury together with the promised money.

He was commissioned: “To bring to perfection an engine for calculating mathematical tables” That same month he set off on a long tour around the country investigating whatever industrial and other techniques which might have had a bearing on the development of his engine.

During this tour he visited all the major industrial centres in both England and Scotland. It was not until later that year he began work on the development of the full-size engine. He converted the stables at the back of his home in Devonshire Street into a workshop. He hired several workmen individually to carry out specific jobs under his personal directions.

Of course he did not have all the necessary tools or skills himself to build the engine. It was not long, therefore, before he needed the special facilities that only a professional engineer could provide. He was recommended Joseph Clement for this assignment by his friend, Sir Marc Isambard Brunel. Clement, a north countryman, had been employed by the famous machine tool developer, Henry Maudslay.

Later he had set up his own workshop at his house, 21 Prospect Place, near the Elephant and Castle in London. Clement had the reputation of being a meticulous worker as well as being an excellent draughtsman, just the skills Babbage needed for this project. The first designs for the full-size engine were laid down at this period. It was to use 5 columns or orders of Differences in its calculations and to print its results to 12 significant places of decimals. Work continued for some years.

In 1827, however, Babbage suffered a number of personal tragedies. Both his father and wife died that same year. As a result he suffered a nervous breakdown. His doctor advised him to take a complete rest.

Through his brother-in-law, William Wolryche Whitmore MP, he obtained permission from the Chancellor of the Exchequer to take leave from the project In October 1827 he set off on a grand tour of the continent, which was to last for just over a year. Work, however, continued at Clement’s in his absence under the supervision of his friend John Herschel.

All the original monies allocated to the project by the Government had been spent. Babbage, however, had by that time received a large inheritance from his father. He therefore assigned some of this to continue the works. He granted Herschel power of attorney to make the necessary payments to Clement.

During this break he continued to correspond with both Herschel and Whitmore, with the former on technical details and money matters, and with the latter on the fact that the Chancellor in 1823 had made a verbal promise to him during his interview that the £1500 originally allotted to him when he commenced the project would only be the first of many such advances.

Not much happened while he was away. Herschel even remarked that he thought the whole project appeared to be moving far too slowly. He seemed very surprised that there was little to show for the amounts paid over to Clement. Clement in fact, apart from producing a large number of drawings looked to be spending much of his time developing and designing the necessary tools to manufacture the Engine, including a large lathe and later a planing machine.

Whilst he was on the continent Babbage took advantage to visit many workshops, including Gambey’s, a famous establishment in Paris, learning many new techniques which might have relevance or application to the design of his engine. Immediately upon his return to England, at the end of November 1828, he was determined to have the matter of the funding of the project resolved.

Several thousands of pounds were still owed to Clement in spite of the amount he had left with Herschel for payments.

Moreover there were several important matters which needed clarification, such as who owned the tools and drawings, who was responsible for insuring the engine against the risk of fire, indeed who owned the engine at all and so on. He spent the first week in December 1828 preparing a long statement of the situation as he saw it, sending it to the Prime Minister, the Duke of Wellington.

This the Duke passed over to the Treasury for their consideration. They latterly ordered an investigation to be conducted by the Royal Society as to the state of the project. In February 1829 an extremely favourable report was produced by the subcommittee of the Royal Society assigned to review the project.

This was conducted under the chairmanship of his friend John Herschel. Their report outlined that the engine was progressing well; they had ascertained that most of the components for the calculating part of the engine had been made, that nearly four fifths of the designs for the engine had been completed, and that the level of workmanship was amongst the highest quality they had ever seen.

They especially recommended that Babbage should be relieved from the responsibilities of financing of the project from out of his own pocket. As a result of this report the Treasury advanced Babbage a further £1500 in April 1829 to enable him to continue work towards completion the engine. This just about made up what Babbage had invested personally in the project.

It was probably also particularly timely for Babbage, as he was moving house at that time from No. 7 Devonshire Street to No. 1 Dorset Street and needed the funds to pay for it. Clement, however, was still owed some £2052. He had done a total of £5312 worth of work but had only received £3260.

Babbage was determined, however, that he should receive no further monies until better arrangements for the reporting of work done were instituted. Clement was naturally not pleased with this and in May 1829 stopped work on the Engine refusing to do anymore till he was paid. Thus ended the first phase of Difference Engine No 1.

It was not to start up again for another year. Phase II (May 1829 to March 1833) In the middle of May 1829 a group of very influential friends of Babbage’s got together at his house to try and plan a way forward.

They considered many options including the private financing of the project by subscription, to be offered to Babbage’s rich friends. It was decided, however, that the Government should in the first instance be approached to see if it could sort out the mess. Herschel and Whitmore were appointed to meet with the Duke of Wellington to discuss the matter, which they did, discovering him to be quite enthusiastic about the project and sympathetic to Babbage’s plight.

As a result Babbage arranged through the auspices of his friend, Lord Ashley, for the Duke and his Chancellor of the Exchequer, Henry Goulburn, to pay a visit to Clement’s workshop to see the work for themselves. This took place in November 1829. In December the Treasury agreed to advance a further £3000. But the question of who owned the machine still remained open.

In February 1830, at a meeting between Lord Ashley and the Chancellor of the Exchequer, it was agreed that the engine should become public property. It is to be noted that this was not ratified by the Board of the Treasury till December that year. Also in February 1830, having still not had his bill from the previous May settled and after threatening legal action, Clement agreed to have his accounts arbitrated by two referees.

This he had been pressed to do by his professional colleagues. Henry Maudslay and Bryan Donkin were appointed to perform this task. After their report in April 1830 Babbage forwarded Clement the balance owed him. In the spring of 1830 work recommenced on the project. Drawings from this period indicate that a larger machine was being contemplated: calculating with up to 16 digits using 7 orders of differences.

That autumn a new employee was hired by Clement as his principal draughtsman, Charles G. Jarvis. The latter because of his ability was to earn the considerable respect of Babbage and later to be employed by him on the development of the series of Analytical Engines.

During the summer of 1830 Babbage started sending regular reports to the Chancellor, Viscount Althorp, on the progress made. In one of these he advised that, as the engine was now proceeding towards its completion, suitable premises for it should be found to erect it in and operate it from, specifying that, for convenience, it should be set up in the vicinity of his home.

In January 1831 at Brunel’s beckoning Babbage arranged for a local surveyor, Charles Jearrad, to search out for an appropriate site in his area and prepare a report on the likely cost of erecting a suitable building.

The most apt plot proved to be part of the garden and stable yard at the rear of his home. An estimate for the works was drawn up and submitted to the Chancellor, who passed it to the Treasury for consideration.

Again the Treasury sought the advice of the Royal Society on the need for this. In March 1831 they once again reported favourably, remarking that these premises were needed urgently.

Thus in April the Treasury commissioned the Office of Woods and Forests to erect suitable buildings. The latter appointed Decimus Burton, one of the most well-known architects of time, to undertake the work.

After some quibbling on whether permanent workshops were also needed as well as an engine house and accommodation for the engineer, designs for the buildings were complete and construction work began in January 1832.

These were completed as far as they could be without the Engine being in them by June that year. Over £2,000 was spent on the building works. In July 1831 Babbage submitted to the Treasury the first set of accounts for payment for works done on the engine since it had been formally declared public property.

These had already been reviewed by the two professional arbitrating engineers for their accuracy. The Treasury, however, this time ordered their auditing department to examine the details of the bills and prepare a proper statement. This was to be done every time a bill was submitted.

This procedure had the effect of extending the time interval between submission by Clement of his bill and the receipt of payment by an additional 2 to 3 months. Clement was not a rich man and had a workshop of around 10 employees to pay the wages of.

As a result Babbage, to tide him over while he waited for his monies from the Treasury, continued to advance Clement with sometimes as much as £1,000 out of his own pocket.

In September 1831 Babbage had many new ideas for the engine to improve its performance It appears that several major revisions in its designs date from this period: these include changing the number of cycles or turns of the first axis required by the punching department for each result from 24 to 20. Later on the Engine was extended to calculate with 18 digits and not just 16.

On Babbage’s instructions during 1832 Clement began the assembly of a test/demonstration model of the calculating part of the Engine. This was ready by December that year and delivered to Babbage.

This is the small fragment now on view in the Science Museum. It was the only part of the Engine ever put together. It comprises of 18 figure wheels and a special driving department specially developed for it.

It still works well and is convincing that the full-size engine would have worked satisfactorily had it ever been completed. Work thus seemed to be progressing well. Parts were gradually being made, and development seemed to be nearing an end.

That summer Babbage asked Clement to prepare for the removal from his workshop to the new fireproof premises next to his home, where the Engine was to be assembled. He asked him to submit an account of the likely extra costs, expenses etc.

He would incur as a result of this. Clement presented an outrageously expensive claim of some £600 a year of additional costs. Babbage was very angry with him, the Treasury concurring, asked him to present another claim. This he appears not to have done.

In March 1833, whilst Babbage was at Clement’s workshop, Clement asked Babbage, as was usual in the circumstance, for an advance on the strength of his previous bill (for the work done between June and December 1832).

Babbage refused unless Clement withdrew the extravagant claim he had made to work from the new premises. Clement remarked that he did not want to move. A row ensued in which Babbage declined to part with another shilling unless Clement complied with his request.

Clement said that unless he received some money he would dismiss all his workmen by the end of the month. Babbage walked out in a huff. Two weeks later Clement carried out his threat. Work ceased on the engine never to be resumed. Causes of the Failure to complete Difference Engine No. 1 It is often mooted in short accounts and popular histories that Babbage’s First Difference Engine project failed because he had invented a machine with which the technology and workshops of his day could not cope.

This is just not true: had it been completed it most definitely would have worked. The successful performance of the fragment assembled as a demonstration and test piece in 1832, now in the Science Museum London, confirms this point of view.

Rather the project failed through a combination of far more mundane reasons, reasons related to the manner in which the project was organised. 1. Too Frequent Changes of Government Between 1833 and 1835.

Spring-Rice’s Misinterpretation of Babbage’s Intentions. Project in Doldrums 1833-1842. Between 1833 and 1835 there were three changes of Government. This historically was the most immediate reason for the Difference Engine’s failure.

Babbage’s lack of success to get the project restarted caused a loss of momentum. Projects in general seem to require a kind of momentum to keep them going. It is what motivates individuals concerned to get on with the work or maintain an interest in it. As soon as the momentum is lost, the credibility of projects drops enormously.

The rapid and many changes in Government in the period 1833-5 allowed things to slip too much. Several attempts were made by Babbage to get the project back on the road, but none of these came to anything.

The circumstances were these. Work had stopped on the project on 12th March 1833, following the row between Babbage and Clement that day over the refusal of the former to advance the latter any more money out of his own funds.

Clement had made an extravagant claim for removing his business to the new premises, adjacent to Babbage’s house in Dorset Street, to continue work on the Difference Engine at the specially constructed premises there.

The Treasury had criticised this demand and Babbage had asked Clement to revise it. But Clement had not at that time received payment of his account for the work done between June 30th 1832 to the December 31st 1832 and was in no mood to discuss it: he wanted his basic bill paid.

Babbage immediately reported the situation to the Treasury, his sponsors. After an investigation by the auditors the Treasury ordered payment of Clement’s final bill stopped, until he agreed to deliver the finished parts and drawings to the new fire-proof building.

What follows is a chronology of the events in this story as they occurred. One will see clearly from these that the three parties concerned (Babbage, Clement and the Treasury) each failed to appreciate the others’ positions, and that each was not really communicating with the others.

This lack of communication, probably due to differences in social class if anything, was the primary cause of the collapse of the project.

Other issues raised during this period include the insistence by Clement for someone to be nominated to be responsible to him for the project; his overall stubbornness; the security from fire of the completed parts and drawings; whether Clement should receive payment for either the first period describe above (30th June 1832 – 31st December 1832) before he removed the parts as he had been instructed or whether he should be allowed to receive this payment before removing a single part.

Similar considerations apply to the bill for the second period (31st December 1832 to 12th March 1833). 28 March 1833: Babbage wrote to the Treasury describing how he had been totally unprepared for Clement’s extravagant demands for removing the tools and his workshop to the new premises.

That Clement was generally being uncooperative and that he was demanding payment for his latest bill (30th June – 31st December 1832), as he was in need of money. Babbage agreed to submit this bill to the Treasury, but said he would not advance him any more money out of his own private means, as he had done in similar circumstances in the past. Babbage further reported to the Treasury that Clement had given notice to his workmen.

He was happy to report that a small portion of the Engine, containing 15 figures, had been delivered to him some three months earlier. 3 April 1833: At Babbage’s request Messrs Field and Donkin, the arbitrators, had been to see Clement.

They identified that the main issue that Clement was concerned with was who was responsible to him for the project, the Government or Babbage. 13 April 1833: In a letter to Babbage, Bryan Donkin said that he had been to the Treasury to discuss Clement.

He learned that they would probably concede to Clement’s demand. 25 April 1833: Bryan Donkin reported to Babbage that the Treasury generally had no objection to paying Clement. Clement should however agree to withdraw his offensive letter to Babbage, and that thereafter he should request the Treasury to pay him direct. This being done he was to state clearly that he would be willing to continue work on the machine at his premises in Prospect Place, but as and when parts were completed to deposit these in the new fireproof premises.

Donkin informed Clement of these arrangements.

13 May 1833: Clement wrote to Babbage asking him to be allowed to continue to finish the machine at his own workshop. He hoped that payments thereafter would be made direct from the Treasury to himself. He also requested withdrawal of his letter of the previous July which outlined his demands for the removal of his works to the new premises.

20 May 1833: Babbage wrote to the Treasury asking them to pay Clement direct thereafter, as it appeared, whenever the Government’s estimates were published, that he, himself, had received the money, whereas the truth was that it had been simply paid over to the engineer, Clement. He reported that Clement had requested to be allowed to continue.

20 May 1833 In a second communication that day to the Treasury Babbage suggested the following directions should be given to Clement.

1. That all the drawings not required at Clement’s own workshop should be removed to the new premises.

2. That the drawings necessary for the Engine should be completed as soon as was possible.

3. That all the parts of the Engine already partly executed should be finished as soon as the nature of the work would admit, and be removed to the fire-proof building. He urged that it was important to press strongly on Clement the necessity of dispatch, on account of the danger from fire and the great outlay of public money. He added that he thought the inconvenience to himself might be hinted at, although he considered that that would have but little influence in Clement’s mind.

29 May 1833: Treasury replied to Babbage agreeing from then onwards to review Clement’s accounts in their offices, and pay him direct and not via Babbage. That they agreed Clement’s plan to continue work at his premises and that the parts should be removed to the new premises when they were finished. They ordered Babbage to make the necessary arrangements to receive them. As soon as they were informed that all the parts and drawings that could be transferred without preventing progress they would agree to pay Clement his account to the 31st December 1832.

29 May 1833: Babbage wrote to the Treasury reporting that he had just seen Clement and told him that Clement would be calling at the Treasury. In the same letter he proposed that the drawings should be completed at the new premises and that only working drawings should be sent to Clement’s workshop.

He suggested that Jarvis, Clement’s former principal draughtsman, should be employed by Government to do the drawings under his personal direction, but that Clement should continue to pay Jarvis thereby enabling him to receive the same profit as usual. Babbage saw the advantages of this plan were:-

1. All the most important drawings would be free from danger

2. That in case of further difficulty with Clement the Treasury and he would be much less dependent on him.

3. Were Clement or himself to die it would be most important to have Jarvis 4. Babbage would be much better acquainted with the Engine he had contrived than was possible living as he did far (4 miles) from Clement’s; he reminded the Treasury that his memory, though not bad, could not retain all the relations of 20 or 30 thousand pieces of matter.

Babbage foresaw that Clement would object that this plan would be inconvenient to him. He reminded the Treasury that Clement did not consider that Babbage himself had suffered a similar inconvenience for nearly the previous 10 years.

Clement would argue that it would produce delay and expense. Babbage said that he was more interested than any individual in completing the work and that he believed it would accelerate it instead of delaying it.

The additional expense of Clement’s journeys would not come to much. Finally he suggested that the Treasury should press Clement on this latter point: assuming that no further alterations from the then design would be made, he asked the Treasury to ascertain from Clement how long would it take to finish the Engine.

He told them that he had repeatedly tried to obtain Clement’s opinion on this matter and, given the state of the work as it then stood, Clement ought to have been able to form if not an exact but at least an approximate conjecture. Ca

1 June 1833: Babbage wrote to Clement giving him details of the Treasury’s instructions to move all the parts of the Engine to the fireproof building and requesting a meeting with him proposing dates.

4 June 1833: Babbage wrote to Bryan Donkin telling him that Clement wanted his accounts for the second period (31st December 1832 -12th March 1833) examined. He warned him that Clement was being stubborn and was still refusing to move anything till his demands were met in full. He asked him if he would arrange with Joshua Field an appointment with Clement.

22 July 1833: Clement wrote to Babbage telling him that he had sent a letter to the Treasury asking them to let him know whether they intended to absolve Babbage from having to pay the account up to 30th March 1833. He then went on to say that he has made a proposition to the Treasury. But even if they agreed to it, he told Babbage that he did not intend to absolve him from the responsibility until the account had been paid in full. He warned Babbage that if the Engine was destroyed by fire that he would not be held responsible for making good the loss.

22 July 1833: That same day Clement tried to seek a new arrangement with the Treasury. He wrote to them putting his side of the case. He remarked that in all his dealings he had treated with Babbage, and that he therefore considered Babbage was, as regards the engine, fully responsible to him.

Babbage had always paid his bills, given him his instructions and Babbage had been the one to whom he had delivered a part of the machine. Referring to the arrangement that had been set up in April 1830, when an arbitration procedure for reviewing his accounts had been adopted, from then on it was accepted that after the appointed arbitrators had approved them, it was Babbage who was to pay the agreed sum.

He went on to say that on 8th February 1833 Messrs Donkin and Field had called at his workshops to examine all the parts of the Engine that had been made between 30th June and 31st December 1832.

Having satisfied themselves an account was prepared by 20th February 1833 and delivered to Babbage soon afterwards. But, according to Clement, Babbage had said that he refused to present this account to the Treasury unless he, Clement, made some proposition to them regarding the removal of his business to the new premises.

Clement said he wished to decline this pressing Babbage instead to settle his account. After he had said this Clement reported that Babbage had told him that from then onwards he would refuse to advance or pay him a single shilling.

Clement now asked the Treasury whether it was their wish to continue with the project. He also said that he had asked Babbage whether the machine was the Government’s or Babbage’s property, reporting that Babbage had again refused to answer that question, replying that he had no authority to discuss it.

Clement told the Treasury that he had therefore written to Babbage saying that unless his account was settled in full and unless he received a full declaration of who was responsible for the project that work would cease on the 30th March 1833. No arrangement was made and therefore work had stopped.

Clement said that he understood that the Treasury was still refusing to pay his account if he did not remove the finished parts of the Engine to the fireproof building. He now said he was anxious to receive payments for both the work done between 30th June and 31st December 1832, and also for work done in the period after.

As Donkin and Field had examined and approved his account up to 31st December 1832 he asked whether the Treasury would oblige by settling that one straightaway. With respect for the work done after 31st December he suggested that, as Donkin and Field were both very busy men and had been unpaid for their services, that then onwards two arbitrators paid by each party be appointed in their stead to review and approve the later account.

That completed he agreed to move whatever finished parts and drawings which would not interfere with the progress of the Engine. Once this was done he hoped the Treasury would settle this last account. He then went on to say that, if the Treasury were willing, he would continue under Babbage’s superintendence at his manufactory in Prospect Place, delivering the finished parts to the new premises after they were made and after they had been examined and passed by the arbitrating engineers.

And then when the whole was finished he agreed to assemble the whole machine at its new accommodation. He further proposed that thereafter two engineers should be appointed, paid for by each party, to examine the progress made and prepare the account every three months.

That the account was to be reviewed within a month of its being made and that a complete settlement should be made immediately afterwards, if the engineers agreed to it. And if they did not it was to be submitted to a third for arbitration. That no one thereafter would to be legally justified in withholding payment. Clement further warned the Treasury that he was not liable to replace any part that might be destroyed by fire.

29 July 1833 Babbage reported to the Treasury that he had had an unsatisfactory meeting with Clement after their letter to him of 29th May 1833. As a result he had asked Clement to express his views in writing. 8/9 August 1833 Marc Isambard Brunel recommended that Babbage consider an alternative workman to Clement suggesting a man called Spiller. Advised him to be absolutely firm with

Clement: to make no payments until all the components etc. were brought into a safe fire-proof place.

17 August 1833 Treasury demanded Babbage take the necessary steps for the removal of the completed drawings etc. to the new building. With respect to Clement the Treasury ignored some of his requests, saying that they preferred to continue to use the free services of Donkin and Field as arbitrators.

Neither did they answer all his questions. They did, however, agree to pay him his account up to the 31st December 1832 (without him having to transfer any of finished parts or drawings to the new premises) and told him that they would consider payment for the account for the later period, after he had complied with their request to move those parts which could be removed without impeding progress on the machine to the fireproof premises.

25 August 1833 C. G. Jarvis wrote to Babbage suggesting a new arrangement for the work. That if the Engine was to be finished within a reasonable amount of time, all the designs and drawings ought to be undertaken at Babbage’s home under his immediate supervision.

Time wasted because of Babbage’s absence could thus be minimised. And any working drawing or works order made from them could then be sent out to several different workshops so that the various parts of the Engine could be made at the same time. He continued by saying that the calculating part was the only part in which anything of consequence had been done.

That it was the simpler when compared with printing department; the latter whose arrangements, construction and settings were far more difficult to comprehend. He warned Babbage that he personally might be out of the country by the time work recommenced on the engine.

11 September 1833 Jarvis wrote to Babbage. He realised that Babbage was of a mind to want to complete the engine and that Clement was probably bound in justice to construct it if requested, as he has all the specially made tools necessary for the job. But he warned Babbage that he could not be expected to make any personal sacrifice just because he was the draughtsman.

He pointed out that all the praise would attach to Clement on its completion and little or none to him as an employee. He did not want to degrade himself. 4 December 1833 Babbage ordered Clement, as preparations for removal of the engine were complete, to carry out the following instructions:

To move all parts of the engine except the large platform for the calculating end and the large columns; all the drawings, (the 27 still attached to drawing boards were not be taken off them, Clement was to include cost of the boards if necessary); all the rough sketches, small notebook on contrivances determined upon and the several loose sheets of mechanical notations of the Engine; and all the patterns from which castings had been made and thus were no longer required. He was also to oil all the parts made of steel and pack them to avoid rust and to supply a list of the parts remaining at his workshop, but belonging to the Government.

30 January, 1834 Clement wrote to the Treasury telling them that everything was ready for removal. He explained that would be more convenient to him if those parts that were made during the period from end 1832 to March 1833, which were still unpaid for, were examined at his workshop before they were packed.

8 February 1834 Treasury wrote to Babbage asking him to apply to Messrs Donkin and Field to examine Clement’s accounts. They also asked him to prepare to satisfy himself all was in order when delivery to the new premises was made.

10 February 1834 Babbage wrote to the Treasury explaining that heating was wanted for the new premises, rates and taxes on it needed to be paid for and a watchman was required. Treasury replied explaining that they would direct the Office of Woods and Forests to take charge of the building and arrange a budget to charge costs of it to.

14 February 1834 Babbage wrote to Donkin asking him to arrange a mutually convenient time with Field to examine Clement’s accounts.

6 July 1834 Babbage wrote to Donkin asking him and Field to inspect the content of boxes against Clement’s list now that they had at last been delivered to the new premises. This was required urgently as the Chancellor of the Exchequer and Lord Lansdowne wished to see the Engine and Babbage did not want to open the boxes or touch anything till the inspection had been done and the list checked. 8 July 1834 Babbage asked Field with Donkin (see above) to compare Clement’s list with the content of the boxes in Clement’s presence.

16 July 1834 Babbage explained to the Treasury that all the completed parts of the engine had now been safely delivered to the new premises. Would they give him further instructions.

That same day Lord Grey’s administration fell and Lord Melbourne was appointed Prime Minister. Viscount Althorp continued as Chancellor of the Exchequer. During the latter half of 1833 Babbage and his son had helped Dr Dionysius Lardner, a well-known populariser of science, prepare visual aids and other materials for a lecture on the Difference Engine.

He had shown an interest in the subject for some years. Lardner’s planned lecture tour took place during the first half of 1834. He visited many of the major industrial cities of England, presenting his talk at the various Mechanical Institutes and also the various premises of the Royal Institution. His lectures were well received.

In July 1834 a long article by him on the Engine appeared in the Edinburgh Review. In it he complained of the lack of attention that the Government were giving Babbage and his Engine. In August 1834 Clement received his last payment from the Treasury after Babbage had confirmed that their demands had at last been fulfilled.

The Government’s total outlay on Difference Engine No. 1 had, by that time, been £15,288-1s-4d on the development and engineering work and a further £2190-13s-6d for the special buildings. In September Babbage wrote to Lord Melbourne to ask what was to be done, urging him to come and see for himself the state of the machine. Lord Melbourne replied that he would very much like to.

But Babbage was out of town at the time when his letter arrived, presumably attending the funeral of his daughter in Worcester. Thereafter, Melbourne was too busy to deal with the matter, and in December 1834 his Government fell: Viscount Althorp had been raised to the peerage following the death of his father and the king had used this as an excuse to dismiss Melbourne. The reins of power passed into the hands of Sir Robert Peel.

In December 1834 Babbage wrote to the Duke of Wellington asking him to take up the matter with Sir Robert Peel, as he felt that the latter might not be sympathetic towards him. The Duke asked Babbage to make his wishes and objects more clearly known in written form.

As a result, on 24th December 1834, Babbage drew up a long statement of the circumstances of the Difference Engine addressing it to the Duke. In it he explained that he had taken up the project some thirteen years previously at the wish of the then Government.

They had agreed to sponsor it because it was of a nature such that it would not a profitable scheme for private enterprise to consider; rather it was very important for a country, which had a large fleet of ships, to add to its security by having error-free astronomical and nautical tables.

This, Babbage thought, were statesmanlike reasons. Neither had it been taken up as a personal favour to Babbage, even though he was of liberal principles, but more for the benefit of the country. At that time Babbage considered that the project would only last two perhaps three years.

With that in mind it did not occur to him to charge a fee for his services or demand any honour. As it turned out, however, he was to work on it for above 10 years amid considerable difficulties in the attempt to complete it.

Six governments had come and gone during that time; he had communicated with them all about the work, but found that he had several times to fund the project using his own money and resources to prevent delays which would have otherwise occurred, whilst waiting for the Treasury to act.

Now work had ceased altogether, after he had refused to make any further advances out of his own monies to Clement. Babbage complained that both he and his engine had been ignored both by the Government and the nation at large. He told the Duke that during its construction he had spared no expense looking for manufacturing techniques to improve the Engine.

He had traversed the whole of Europe in the search for these. Many novel devices had subsequently been incorporated in it design. He had even written a book, Economy of Machinery and Manufactures, describing many of his findings; this had since been translated into many languages.

Consequently it was to be noted that many European governments were not unaware of the project. He went on to explain that he had also turned down a number of offers for positions of considerable reward in the City, e.g. one in 1824, which would have paid him a salary of £2,000 p.a. (as an actuary in a life assurance house), because he felt honour- bound to devote all his energies to complete the Engine.

In 1832, when all the designs for the Engine had been completed, he had constructed a small test engine. This worked perfectly, fully demonstrating he would have been able to meet all that he originally promised and more.

After this he had expected some recognition from Government for all his labours, even though he had not been promised any. After all this model represented the first example ever of the conversion of mental into mechanical processes.

Neither had Government protected him from public criticism. Both Tories and Radicals had claimed he had been pocketting public money, whereas the real truth was the complete opposite.

Other countries, even the smallest in Europe, would have paid more attention. Of the seven prime ministers that had been in post since the commencement of the project only he, the Duke of Wellington, had been to see for himself the progress being made and appreciated the worth of the Engine.

Babbage went on to report that 12,000 parts had been made, that the drawings had four months previously been deposited in a fireproof building, and that the buildings to receive the completed engine, workshops and a house for the superintendent of the Engine were all finished and ready.

He then outlined four ways the Government could proceed: a) To continue as before with the same engineer (Clement). Babbage thought this option was really a practical impossibility.

Circumstances had arisen over which the Government and he had no control, which rendered it highly inexpedient. (Viz. difficulties of dealing with Clement and the fact that Clement’s staff and their skills had since dispersed all over the country to other workshops).

He said he would probably be willing to continue on this basis, if that were the only course open, although he construed that to be the worst possible interpretation of the agreement which he had made with Government at the start of the project.

Rather he preferred to dismiss this option altogether. b) To appoint another competent engineer to complete the work. Babbage said that he had spent some time reflecting on this and concluded that it was feasible; moreover it might well prove to be less expensive and that the engine could probably be completed more quickly.

But it would also involve him in further personal sacrifices, which, after what he had already experienced, he did not think he was under any obligation to make. He was ready to explain his reasonings and the means by which Government could complete the Engine, and to consider, in this respect, any proposition the Government might make, but would not suggest any himself. c) To appoint another person to oversee the project in his place using his designs and drawings to complete the engine.

Again he considered that this was a feasible option, but that the Government would probably think that inexpedient.

If, however, they thought otherwise, he said that would be ready and willing to transfer the engine to anyone they chose to nominate. Or d) Government could decide to give up the project altogether, even though this might expose them to some political criticism in Parliament, as it might be considered that a large sum of public money (some £20,000) had be squandered in some useless and absurd speculation.

Babbage presumed that both political parties would want to be rid of their portion of the blame for it and that eventually they would unite in using him as their scape-goat. He remarked he had experienced the injustice of his countrymen before and would not shrink from it again.

He then alluded to the fact that, in the meantime, he had invented an altogether new calculating engine. It was difficult for him to explain his feelings and motives, but for the two years since work had stopped on the old engine he had been deprived of the drawings.

Four months earlier they had been returned to him. He then had proceeded to re-examine and criticise every part.

This exercise had resulted in his being able to create a completely new machine in which every part was novel and none of which was used in the original engine. Although it exceeded in power the old one he explained that it was not intended to supersede it, but rather to extend its power and utility.

He intended for the time being to give up all other pursuits and devote all his energies and efforts to the development of the new engine.

He had hired a competent draughtsman (C.G. Jarvis) and had advanced considerably with the drawings.

The great mechanical principles on which it depended and the contrivances which controlled its action had already been decided upon.

It was his intention to proceed to finish the drawings in such a manner that the whole invention of the new engine would be complete and susceptible of being executed at a later period.

But whether he would personally be able to afford to construct such a machine, as his own private resources had been injured by the sacrifices he had made on the former one, was not certain.

He warned that it was not inconceivable that another country forming a different estimate of it value and utility might approach him.

Furthermore it was to be noted that he was within his absolute rights to dispose of his invention as he saw fit.

In the event he would collect together all that was best in British industry, both methods and processes, which, by this means, skills and knowledge would be transferred to that other country to its benefit, more valuable than the engine itself perhaps in promoting its industry.

He went on to remark that the men who had formerly been employed on the engine and who had since scattered to the various industrial centres around the country, they received higher wages than other workmen as a result of having worked on the Engine.

But Babbage could not make any claim on the Government as he had not originally agreed to any. If it had cost the Government some £20,000, then it had cost him a great deal more in lost income.

All Babbage wanted was a decision as soon as was possible on the future of the engine as new arrangements were necessary. The Duke of Wellington acknowledged receipt of the statement, but said he personally could not act.

Nothing further took place for three months. In March 1835 Babbage was advised by his friend, Benjamin Hawes MP, once again to approach the Government as it was of a reforming character. In April 1835 he wrote to Sir Robert Peel enclosing a copy of his statement to the Duke of Wellington.

But this time Sir Robert Peel’s Government also fell and once again Lord Melbourne’s was back in. Babbage’s papers were thus passed to Thomas Spring-Rice, the new Chancellor of the Exchequer, (a Cambridge man and an acquaintance of Babbage’s from previous elections which had been held in that city) to deal with.

In May 1835 Spring-Rice announced to Parliament that the Government proposed to spend another £1500 on the project; note, no consultation had taken place with Babbage on the real amount required.

Be that as it may, Parliament refused to sanction this until a review by the Royal Society of the project had been undertaken. They probably made this suggestion as the Royal Society had in the past been asked to advise various Governments (in 1823, 1829 and 1831) what to do.

Babbage, however, disagreed. He asked for a personal meeting with Spring-Rice to explain his views. At that meeting (held on 26th May 1835) he told the chancellor that he thought the Royal Society was not a suitable agency on which to rely for opinions on his engine as:

a) they were not workmen

b) the process would take too long and cause another three months delay

c) Some FRS’s were either hostile to him or jealous of his abilities

He also tried to explain the causes of the delay. Clement was a slow worker. It was in his interest to cause delay. That he was obstinant in his refusal to allow Babbage to have the drawings for a year and a half.

He had made excessive demands on the Government to ensure that work was retained at his premises in Prospect Place. That everyone who had come into contact with him was discontented with him. And that the Engine itself was completely new and quite unlike all previous machines.

Babbage suggested several ways forward The tools should now be kept at his house The Government should appoint Jarvis to superintend and make it his interest to complete the work. In place of the Royal Society a committee of professional engineers should be appointed to review the engine: he proposed Rennie, Cubitt and Brunel. However it seems that Spring-Rice did nothing after this meeting.

In November 1835, Jarvis, Babbage’s draughtsman, was offered a job overseas (in France on a railway project) at a very lucrative salary.

Babbage tried to contact the Government warning them of their pending loss if they did not continue to employ Jarvis, who had acquired all the knowledge and skill associated with the engine.

Spring-Rice, however, was out of town at that time. Babbage, therefore, who had already hired Jarvis on his own account to work on the designs for the Analytical Engine drew up a new contract with him, paying him a guinea for an eight hour day and binding him not to leave his employment without giving some considerable period of notice, six months.

In January 1836 Spring-Rice’s private secretary acknowledged receipt of Babbage’s letter, explaining that Spring-Rice had been out of town unwell.

He reminded him that Babbage had not yet agreed to make his statement to the Duke of Wellington an official communication, i.e. have it registered by the Treasury.

Until that had been agreed the Government could not really act upon it. Babbage, if he preferred, could draw up an alternative statement.

But he also added that as Babbage had invented another more powerful engine was he asking the Government to sponsor that instead. He again raised the issue that Parliament had asked the Chancellor to arrange for the Royal Society to investigate the progress made on the machine and how long it might be before it could be expected to be completed, and that this was the course he expected to pursue.

Thus it seems that Babbage had confused Spring-Rice, by mentioning the newly invented Engine. Even though Babbage was at pains to explain to the Chancellor that the old Engine would still work and work as well as he had always promised, the invention of the new one probably killed the credibility of the former engine in the mind of the politician.

Indeed Babbage was, later on during 1836, looking at the possible development of a new form of difference engine based on the principles he had developed during the previous two years whilst working on the Analytical Engine.

In his reply to Spring-Rice he had mentioned that it would probably be cheaper to scrap the old engine, and begin again using the new principles rather than continue work on the old one.

This confronted the politician with a quandary: could the Government face the criticism of having wasted thousands of pounds of public money by scrapping the old engine? or should they invest in a completely new one, also likely to cost thousands of pounds? It seems that members of Melbourne’s Government had not got the moral strength to cope with such dilemmas.

Nothing more was heard from them for two years. Babbage once again tried, in July 1838, to get Lord Melbourne and his Government to arrive at a decision on the Difference Engine, reminding them that if the decision had been made more difficult it was because they had delayed in coming to one.

Again Spring-Rice replied asking Babbage what did he want the Government to consider. He thought that the House of Commons would object strongly if the old machine were abandoned and the new one started.

He asked Babbage to cost both proposals. Babbage replied that there was some confusion. It was only expressed his opinion that it would cost less to throw the old machine away and adopt the new one.

He explained that he had not applied to the Government to construct the new engine, but merely thought his duty to mention that it existed. He went on to say that he did not consider himself sufficiently expert enough to cost the proposals. What he really wanted was a decision on whether he should continue to superintend the construction of the old engine or discontinue altogether.

Melbourne’s Government, however, did not seem to have given Babbage an answer to this. Melbourne’s Government fell in late 1841.

In January 1842 Babbage once again wrote to Sir Robert Peel, the new Prime Minister, to ask what was to be done about the Difference Engine.

Peel was in fact familiar with the project since its conception. He had been approached by Gilbert Davies for support for the project early in March 1823, but was known not to be very sympathetic to it.

But again Peel was too busy to deal with the matter personally. Sir George Clerk, Secretary of the Treasury, was directed to respond to Babbage.

In a letter to Babbage Clerk once again raised the issue whether he was asking the Government to decide between completing the old Engine or constructing a new one based on the simpler principles, which he said Babbage had suggested the cost of which would not exceed that required to finish the old one.

Babbage explained to him that the question he wanted decided was exactly the same as that he had posed earlier to Lord Melbourne in 1838, that Clerk’s assessment of the cost of completing the old Engine (£8000) was misleading based on old reports made by the Royal Society, which were not accurate. In his opinion it would cost as much as had already been spent, ca £14,000 to £17,000. By July Babbage was getting impatient as he still had not received an answer.

In September of that year, however, the Chancellor of the Exchequer, Henry Goulburn, asked the two most eminent astronomers in the country, G.B. Airy the Astronomer Royal and Babbage’s old friend Sir John Herschel, on what they believed the utility of continuing work on the project might be.

The first replied thinking it was humbug and a waste of public money. Neither was the latter particularly enthusiastic as he might have been expected to be, adopting a rather cautious point of view in his reply: he urged the Government to consider its value as measured by its utility. That the £16,000 suggested should be cost-benefitted against its likely output. It seems that these opinions were kept secret from Babbage.

Babbage approached a former Cambridge acquaintance, Sir William Follet, who was closely connected with members of Peel’s Government to negotiate a better deal for himself with the Government.

Babbage had remembered that during one of the Duke of Wellington’s visits to Clement’s workshop, of which he had made several, the only Prime Minister to have done so personally, the Duke had suggested to him that when the Engine was complete he might apply to Parliament for a reward.

Lord Ashley confirmed that there had been some such kind of understanding. This promise, alas, had not been recorded. Neither was it kept.

On 3rd November 1842 Babbage was told by Goulburn that the Government had decided to abandon the project, on the grounds that they considered it too expensive to complete. He offered Babbage to keep the parts of the Engine that already made, ‘in the cause of science’.

Babbage declined this. On 11th November Babbage managed to secure a personal meeting with Peel on the matter of his reward. Babbage felt hurt that he had been left out amongst all his friends and colleagues, who, over the years, had been given titles, honorary appointments and emoluments for what seemed to him to be less public work than he had contributed.

Peel did not agree with him. A row ensued during the meeting, leading to Babbage walking out on Peel. As it happened Babbage purchased the parts of the old Engine at their scrap metal value from the Government out of monies they owed him for maintenance of the premises that had been built for the engine.

These latter the Government arranged to be let, Babbage taking the Engine House as his workshop and another engineer taking the Workshops that had been erected. The principal drawings and the 1832 fragment were transferred to the King’s College museum in the Summer of 1843.

2. Other Reasons for Failure

a) Poor Organisation of the Treasury The Treasury was overworked and understaffed at that time with respect to the volume of work it was expected to undertake.

During the period when the work on the Engine was in progress the Treasury itself was handling well over 25,000 registered items per year. Each of these had to be dealt with by the Board individually. There appeared to be little delegation of responsibility in the department.

No individual item could be given the time or consideration it deserved. Indeed the project was probably taken up by the wrong Government agency. It should really have been placed under the auspices of the Board of Longitude or the Admiralty from the start. There was a complete lack of the definition of roles, responsibilities, authorities etc. at the project’s commencement.

These all had to be worked out as it progressed. For instance, Government sponsorship for the project started in 1823, but it was not until 1830 that it was clear that they owned the Difference Engine Moreover the Treasury was staffed by clerks. None of their people had the skills needed to supervise the project. No one person in the Treasury was given that specific responsibility.

There was a total lack of provision of proper financial planning and management by the civil servants, especially at the outset.

During its progress there was a total lack of project management practised by the Treasury. The auditors they employed carried out little more than a book-keeping exercise, merely confirming the amounts spent.

They, in particular, failed to provide the decision-makers on the Board with the information needed, on the stage the work had reached or the likely future expenditure on the project.

Indeed the Government seemed to have abrogated several of its management responsibilities, handing many of these over to the Royal Society, and expecting them to make their decisions for them.

In consequence the Treasury failed to provide a proper cash base and working capital for the project. All payments they made in arrears. As a result there was a lack of cash flow.

This exacerbated the problems and difficulties Babbage had in his relations with his engineer and caused the crisis which terminated the project.

No one in Government, except for perhaps the Duke of Wellington, championed the project. There were no real scientists in Government and few in Society.

Moreover none of the Governments of the period were particularly stable. There was little continuity in personages at the top of each. Babbage really ought to have restated the benefits derivable from the engine to each government as it was installed.

He failed to do so. The project went on for too long. Babbage presumably lost interest after the Analytical Engine was invented, though he probably felt honour-bound to complete the Difference Engine if he were asked to.

b) Clement’s Monopoly of Production Babbage having more or less decided to employ Clement as the sole engineer on the project and the latter having been allowed to work on it for a very long time, meant that Clement, in effect, gained a full monopoly over its production.

Clement probably was aware of this and charged a much higher rate for his services than if the construction of the parts for the Difference Engine had been let in open competition. This perhaps did not matter much as long as it was intended that Clement should complete the job. But as soon as a contractual difficulty arose between Babbage and Clement then this issue became of fundamental importance to its outcome.

In those days there was no such thing as precise standard measures in use in Britain, no accurate official inch or foot. Accurate national standards in these were not to be established till later on in the 19th century. At that time each workshop more or less had its own benchmarks. The parts made for the Difference Engine had all been more or less adjusted to Clement’s own standards, and machined using his tools and techniques. The drawings and so on were all made using his rulers.

The calibration marks on these latter, their having probably been hand-made, were not necessarily exactly the same as those to be found in other workshops. Of course Clement owned his own tools, even those made for the production of the Difference Engine at the Government’s expense: this was the custom and practice of the trade.

The calibration of the machines and tools used in other workshops may have been close to Clement’s, but probably not near enough the same. Thus parts for the Difference Engine, had they been made in another workshop, would probably not have fitted together well enough with those that had been made in Clement’s.

Therefore it was not practical for another workshop to take over the work after it had been abandoned, without having to remake a large number of its parts.

In reality, however further research is required to establish whether there is any significant truth in this and to identify where this consideration might have been critical to the outcome of the Difference Engine had historically Babbage taken an alternative course and let the project to another workshop. Other workmen did, in fact, offer to take on the work, even at a cheaper rate than Clement (cf. Wright’s, a former employee of Clement’s, offer: some of his tools had been made in Clement’s workshop and he claimed that they were close enough to Clement’s standards).

Sir Marc Isambard Brunel even suggested a workman by the name of Spiller should take up the work. Babbage even interviewed him. Their offers, however, were not taken up. Though Babbage probably considered them very carefully, before turning them down. Babbage wanted Jarvis, Clement’s former principal draughtsman, to manage the completion if work were to have been resumed.

c) Lack of Formal Contract for Project Clement was a pretty stubborn business man. He had made a success of his career and come up the hard way. He was a northcountry man, who had come to London to make his fortune. He had worked in Henry Maudslay’s workshop for a number of years before striking out on his own. Babbage’s project was the biggest and most expensive contract he ever undertook.

But Babbage, in fact, had not drawn up a formal written contract with him, and thus there were no penalty clauses for delays, no rewards for progressing the engine towards completion.

Clement was not motivated financially to complete the job. It suited him to carry out the work at his own pace. If blame is to be apportioned, however, then it was really the Government’s fault that they didn’t press for a formal contract. It was their responsibility to have insisted on one being prepared once it became clear that the engine was their property.

d) Clement’s Illnesses Clement was frequently very ill during the early 1830s. His illnesses caused several disruptions to the progress of the project. These combined with the pressures of work may have contributed to his volatility of temperament, especially when dealing with a person such as Babbage.

e) Babbage’s Own Theory: Conspiracy, Misinformation It is not surprising that Babbage formed his own opinions on why the project failed. He believed that the public had been misinformed about his project. He experienced some of their incredulence in the form of heckling on the hustings at Finsbury during those elections in which he had stood for Parliament and lost. The public believed that he had squandered and/or pocket the money for the project. Babbage had his own theory why the Government lost interest in the project.

He sensed there had been a conspiracy of fairly well-connected scientists working against him, who had spread false rumours and misinformation about the project, contending that they believed it to be a humbug and sowing seeds of discontent and dissension amongst the scientific community. Babbage became quite paranoic about this connivance, developing a strong persecution complex over it.

The two persons he suspected most (and he had received several confirmatory reports of it from his friends) were Sir G. B. Airy (the Astronomer Royal) and the Revd R. Sheepshanks (later Secretary of the Royal Astronomical Society), both persons whom one might expect to be very enthusiastic about the success of the project’s outcome. But both were the sworn enemies of Sir James South.

They had been used as expert witnesses at a case, an arbitration between Troughton & Simms and South, involving the failure of the mounting of latter’s equatorial telescope to operate properly. The former gentlemen had been responsible for constructing it. Sir James was trying to make a claim. Babbage had taken up Sir James’ side in the issue and used his influence to embarrass the two astronomers.

They probably decided to do their utmost to ruin Babbage’s reputation in whatever manner seemed suitable.

f) Instruction to Perfect Engine Lastly Babbage, at the very beginning of the project, had been given the instruction by the Treasury the wording of which was “to perfect the Engine”. He probably took this direction too literally.

Instead of concentrating on developing a working engine with more limited capabilities and facilities, one which might have been completed much earlier. Babbage, being the sort of person he was, spent too much of his time and effort ever trying to perfect and improve the principles of the Engine, its features and its operations. West Hampstead November 1990

– posted by Jim Roberts @ Thursday, February 17, 2005 3 comments

Wednesday, February 16, 2005

Babbage’s First Difference Engine: How it was intended to work

Babbage’s First Difference Engine: How it was intended to work Introduction In 1821 Babbage invented an Engine to manufacture error-free mathematical tables, Difference Engine No.1, the world’s first programmable automatic digital calculating machine, in which the only human intervention was the setting of the machine at the start of the production of a table and the turning of its handle. It was a machine embodying the mathematical principles of the Method of Differences using only mechanisms for addition repeated many times over. For over 12 years he laboured on its designs, securing Government financial backing to build a full-size version. This was eventually abandoned in 1833 uncompleted, after a row with Joseph Clement, the engineer appointed to construct it. During his lifetime he left no published full technical explanation of how it was intended to function. Based on Professor Bromley’s and my own recent studies of the surviving drawings and manuscripts now in the London Science Museum, this lecture attempts to pay homage to Babbage on the occasion of his bicentennial by completing what he was unable to do then, by giving as comprehensive as possible, in the time and space available, a description of how its parts interacted to produce the desired result.The version of Difference Engine No. 1 described here will be that developed in the latter years of the project, around 1832/33, as fairly complete particulars of this model are to be found in the archive. Details of the earlier versions, which are different, are somewhat scant.

Overview of Engine

The engine itself would have stood 9′ high by 9′ long and been 3’3″ deep, having the appearance from the front of the shape of an “L”. The main divisions to be found in the engine: the Calculating Part to the left, the Printing Part to the right, a part which interfaces the two and the framing and chassis running on castors which supports the whole. The principle material used in its construction for all moving parts and support was Gun Metal: a very strong bronze-like substance comprising approx. 85% copper, 12% tin and 3% lead or zinc for self-lubrication. Otherwise French steel was used in the manufacture of the shafts and axes. Approximate overall weight of the Engine, some 4 tonnes.

DE1 was very much more complex in its design than its later sister, DE2, having of the order of 25,000 parts, but would have been very much slower. Its rate of production would have been around 4 digits punched per minute. DE2 would have worked some 20 times faster. At the time of its abandonment some 12,000 parts had been made: the Government having spent £15,288-1s-4d on its development and construction excluding building works.

Each part had its own name. The names used in this paper, if known, are those used by Babbage himself or Clement. They have no equivalents in today’s technology.

The intended produce of the engine was copper plates punched with all kinds of mathematical, astronomical, navigational or business tables, in a form suitable for producing stereotype.

Operating Cycles

For a better appreciation of the action of the parts in DE1, it is essential to have an understanding of its Operating Cycles. Difference Engine No. 1 can be considered as having four levels of basic operating cycle:

1. Turns of the First Axis 2. Result Cycles 3. Line Cycles 4. Block Cycles

These cycles are somewhat analogous to the second, minute, hour, day etc. cycles in a clock.

Turns of the First Axis DE1 was intended to be operated manually by discrete, whole turns of the First Axis by means of its Driving Handle, the prime mover and source of power for all the parts in the Engine. The cue for the timing of their movement was to be taken from its rotation of the First Axis and the parts set along its length. A Turn of the First Axis was required to punch one digit.

In the timing diagram on the Mechanical Notation BAB.[U11] Babbage has further subdivided this cycle into tenths, to show the detailed timings of the movement and interaction of components in the engine. This was the smallest time unit he considered when designing the Engine.

Result Cycles These are the fixed number of turns of the First Axis required to punch one result on the Stereotype Copper Plate and to calculate the next. The operations of punching and calculation may overlap to the following extent. DE1 wants to punch one digit on each and every turn of the First Axis. Calculation may also take place at the same time as punching subject to the following constraint: the reading off of numbers for punching from the Engine’s Table or Result Axis during those turns of the First Axis when it was either being added to by the 1st Difference Axis or on the subsequent turn when the carriage of tens was being resolved on it was not allowed, as the Calculating Wheels were not necessarily stationary at these periods, which is a must for the punching process. These two turns, however, were not wasted. They are used to reset the printing mechanism to begin the punching of a new result, and also, if the engine has just come to the end of punching a line of results, to back the Copper Plate and feed a new line, which actions also require two turns of the First Axis. During these two turns DE1 completes the calculation of the new result.

The length of a Result Cycle is thus dependent on the number of digits per result being punched expresssed in the following formula

The No. of Turns of the First Axis in a Result Cycle = No. of Digits Punched per Result + 2.

This, however, assumes that the number of turns required for each complete calculation within a Result Cycle, the Calculation Subcycle, is less than or equal to the number of digits being punched. In most instances of the use of the Engine this would have been the case. In all normal calculations using the method of differences the calculation subcycle would have been 4 turns of the First Axis. However if only First Differences were being added to the Table Axis this is reducible to 2 Turns. Or, if special calculations are being performed, which DE1 was programmable for, say 2 additions of the 2nd Difference Axis to the First for every addition of the First to the Table, and the like, then the Calculation Subcycle may be more than 4 turns. If the number of turns for the Calculation Subcycle exceeds the number of digits to be punched then it determines the length of a Result Cycle.

DE1 was capable of being run using two different lengths for the Result Cycle: an extended and an abbreviated Result Cycle. This feature was incorporated in its 20-Axis and 3-Figure Motion Departments, which are described later. Its purpose was, for example a table being punched to 8 significant figures, to allow only the least 4 to be punched during most or abbreviated Result Cycles of 6 turns of the First Axis, but when at the beginning of a new line to use a longer or extended result cycle of 10 turns of the First Axis to punch all 8 digits, when and if any changes in the value of the first 4 had taken place. This procedure was designed to save a great deal of time in the punching of tables, roughly 30%, as well as making them more readable. This saving would have amounted to several weeks of work if the table being prepared took several months to complete.

Abbreviated Result Cycle 6 Turns of First Axis Turn of First Axis Calculation Punching of Result 1 No Calc. 5th Sign. Digit 2 No Calc. 6th Sign. Digit 3 Calc.} Calculation 7th Sign. Digit 4 Calc.} Sub 8th Sign. Digit 5 *Calc.} Cycle Reset (and new line if at end of line) 6 *Calc.} Reset (and new line if at end of line) Note: * = Calculation on Table Axis

Line Cycles A line of results punched across the width of the Copper Plate constitutes a Line Cycle. In the printing of a table of logarithms 10 results might be considered a suitable format. Setting DE1 to punch one extended Result Cycle followed by 9 abbreviated Result Cycles, the last one containing instructions to back the Copper Plate to the beginning of the line and feeding a new line would achieve the necessary layout. Other kinds of table, say trigonometric functions, could be set for a different layout, of say 12 or 15 results across the page. Standard spaces between results are introduced whilst DE1 is punching. Larger spaces can be left after a specific number of results, say 5, have been punched by means of the pattern of studs on the stud wheel controlling the Zig-Zag Motion Crank.

Block Cycles After a specific number of rows in the table have been punched, say 5, 6 or 10, DE1 can be set to feed a larger new line, to allow for a gap between blocks in the table. This constitutes a Block Cycle.

Note: DE1 had no End of Page Cycle. When the punching of a whole sheet of copper was finished the operator of engine would have had to reset the copper plate carriage manually to the top of a new copper plate.

Control Mechanisms

Control Mechanisms: DE1 principle control mechanisms comprised the following:

Sine Qua Non Wheels – a pair of cams, one of which was movable the other fixed, which could be sandwiched together to extend or reduce the eccentricity as necessary.

Stud Wheels – wheels carrying an alterable pattern of studs acted upon by roller levers for putting various parts in gear at specific times.

Mechanical Logic: Much of DE1’s control used the equivalent of an AND-gate. This is illustrated by the following where Part A drives Part B in which a control mechanism puts them in gear with one another.

Part A Control Part B Moves In-gear Moves Not Moving In-gear Not Moving Moving Out of Gear Not Moving Not Moving Out of gear Not Moving

CALCULATING PART

Drive for the Calculating Mechanisms

Running under the Engine beneath the General Platform is the Great Axis. It is driven by a wheel fixed on it called the Great Wheel. The Great Wheel is driven by a Pinion fixed on the First Axis placed in/out of gear by a stud wheel in the 2nd 20-Wheel Dept. The overall gear ratio is such that one half turn of the Great Axis is made for every turn of the First Axis. This provides all the calculating mechanisms in DE1 with all the power needed to move them, and, at the same time, gives them the correct amount of angular rotation, for most require a distinct movement of 180 degrees at a time each. The Great Wheel completes its movement at the end of the 9th tenth of a turn of the First Axis; the Pinion is out of gear with it during the 10th tenth of a turn of the First Axis.

Timing Diagram of the Drive for the Great Wheel

PINION ON FIRST AXIS GREAT WHEEL Tenths of Starting Normal Starting Normal Turn of Teeth Teeth Teeth Teeth First Axis

A wheel on the Geat Axis drives Horizontal Bolting Axis. This latter rotates through 180 degrees for each turn of the First Axis in a Calculation Sub-Cycle.

A Sector Wheel on the Great Axis drives the Horizontal Adding Axis. The Sector is set to come into gear at the start of the first and third turns of the First Axis during a Calculation Sub-Cycle, driving the Horizontal Axis through 180 degrees on these turns, leaving it stationary at other times.

Another sector wheel drives the Horizontal Carrying Axis. The sector wheel is set to act during the second and fourth turns of the First Axis during a Calculation Sub-Cycle driving the Horizontal Axis through 360 degrees at each of these times, leaving it stationary at others.

On each of the horizontal axes are bevel wheels. Each of these is in gear with bevel wheels at the base of each of the vertical axes. When the horizontal axes turn these latter also rotate but these will run loose around their vertical axes unless otherwise acted upon.

Barrels Department

The Barrels control the placing in/out of gear in a fixed sequence, of the Vertical Carrying, Bolting, Adding Axes with the drive mechanisms. The Barrels carry the “program” for the calculation being undertaken by the Difference Engine. This “program” is set up at the start of any table to be produced.

On the front side of the Engine is found the Carrying and Intermediate Barrel Axis. This carries 14 Barrels (7 for the Carrying Axes and 7 for the Intermediate Axes). This controls the timing for the process of the carriage of tens and also the feedback operations via the Intermediate Axes, when the Engine is “eating its own tail”. Connected to it by means of a Communicating Axis on the backside of the Engine is found the Bolting and Adding Barrel Axis. This latter carries 12 Barrels. It is responsible for the timing of the placing in/out of gear of the 6 Vertical Bolting Axes and the 6 Adding Axes. Each Barrel is a drum. Screwed to their curved surfaces are studs. These studs act on levers which via Pin Clutches at the base of each of the Vertical Axes puts those Axes in/out of gear with the bevel wheels on the horizontal driving axes. This is rather like the control mechanism found in a bell-tower carillon.

It is so arranged that in normal difference calculations the Barrel Axes are set to move forward to their next positions twice during every Calculation Sub Cycle of 4 Turns of the First Axis, alternately placing the odd and even vertical axes in and out of gear. This takes place during the last 10th of a turn of the First Axis during the 1st and 3rd turns of the Calculating Cycle

Calculating Mechanisms

DE1 has 7 Calculating Axes each of which has 16 Digit Cells 1 for each decimal place, except for the Result Axis which has 18. Each Cell has mechanisms for adding and being added to. During the Calculating Sub-Cycle each Cell goes through the operations of Bolting and Locking, Half Turn and Adding, and the Carrying of Tens.

Bolting and Locking. Each Vertical Bolting Axis has 16 Fingers projecting from its shaft, one for each Cell in the elevation of the Engine. These are arranged in a spiral around one side of the Axes. These same Axes also carry studs for locking the Lower Adding Wheels. During one Calculation Sub-Cycle each Axis goes through one bolting and one locking operation.

During bolting each of the Fingers successively will push the sliding part of a Bolt in-between the teeth on an Upper Adding Wheel. Where, however, the Figure Wheels stand at zero no bolting will take place in those cases.

During locking the studs ‘lock’ tight all the Lower Adding Wheels on the Difference Axis concerned. These remain locked while the digits are being added to the adajacent axis, after which they are released.

Adding Wheels. Coaxial but running loose on each of the Adding Axes in each Digit Cell are found a Lower and an Upper Adding Wheel. The Lower Wheels are permanently geared to Figure Wheels at the front of the Engine. These register the value of the digit held by the Lower Wheels. Inside each Lower Wheel are fixed two unbolting wedges diametrically opposite one another.

The Upper Adding Wheels have 20 downward-pointing teeth with gaps between them. These are permanently in gear with the corresponding Lower Adding Wheels on the adjacent, next lower Difference Axis.

In between the Upper and Lower Adding Wheel one finds the Bolt. This has a fixed part, which is attached to the Adding Axis, and a sliding part. The Bolts mechanisms are centred on the Axes and, in their starting positions, are aligned horizontally front to back with the Engine.

Half Turn and Add. If on one turn of the First Axis the Bolts have been pushed forward and are now in-between the teeth on the Upper Adding Wheels, on the very next turn the operation of adding will take place. As the Vertical Adding Axis rotates so will the Bolts fixed on it. This drives the Upper Adding Wheels round. When a Bolt encounters one of unbolting wedges it will be become unbolted from its Upper Adding Wheel, no longer able to drive it round. The Bolt, however, continues to rotate with its Axis until it is aligned front to back with the Engine again. A 180 degrees rotation of the Adding Axis has been made: this action is termed a ‘Half-Turn’.

In the meantime the corresponding Lower Adding Wheel on the adjacent Difference Axis will have turned through the same distance as the Upper Adding Wheel, with which it was geared, was pushed by the Bolt. A modulo-10 addition of the digits on the higher difference to those on the lower has taken place: this action is termed an ‘Add’.

Carry Warning Mechanism. If any of the Figure Wheels pass through from 9 through to 0 this sets off a ‘carry warning’. A detent releases an arm pivoting on the Adding Axis, the Carrying Lever. This latter Lever is in conjunction with the Lower Adding Wheel in the Cell immediately above. It registers that a carry of 1 is owed.

Carrying of Tens. On each Vertical Carrying Axis set in a spiral are 15 Fingers projecting from its shaft. When the Axes rotate they do so in turns of 360 degrees. Each of the Fingers acts in succession from bottom to top of the Axis during that turn and picks up all the carriages of tens that are owed. If the Carrying Lever for a particular Cell has been released then the Finger will push it. In doing so the Lower Adding Wheel in the Cell above moves forward one digit. The Carrying Warning Mechanism is also reset. The carry owed has now been paid.

Carriage by Succession. If the Figure Wheel above registers 9, carriage of 1 to it would cause it to indicate 0. Consequently a ‘Carry-Warning’ would have been set in that Cell. This happens before its Carrying Finger reaches it. When it does catch up its Finger acts on the retracted Carrying Lever and adds 1 to the Cell above that. If there was a sequence of 9s before Carrying started and a carry-warning was set in the cage immediately below the lowest in the sequence, carriage would be transmitted via each Cell up the column by the rotation of the Vertical Carrying Axis. This is termed ‘Carriage by Succession’.

1. The above diagram illustrates the Calculation Sub-Cycle (Turns 3, 4, 5 and 6) of a Short Result Cycle (6 turns). In a Long Result Cycle (10 Turns) the Calculating Part of DE1 would be quiescent during Turns 1, 2, 3, 4, 5 and 6 and its Calculation Sub-Cycle would be Turns 7, 8, 9 and 10 with the same operations as shown above.

2. CARRY: Carriage of Tens by Succession. Represents a full or 360 degree turn of the Vertical Carrying (and Figure Wheel) Axes and their Fingers for the Difference concerned. Carrying precedes Bolting during the same phase for each individual ‘Cage’.

3. BOLT: A half or 180 degree turn of the Vertical Bolting and Locking Axis for the Difference concerned, in which the Fingers projecting perpendicularly and in a spiral from the shaft of the Axis act on Bolting Levers which lock the Bolts on the Adding/Calculating Axis to their Upper Calculating Wheels. Bolting succeeds Carrying for a particular ‘Cage’ during the same turn.

4. ADD: In which the Lower Calculating Wheels on the Vertical Adding/Calculating Axis are in such a state as to receive addition (Modulo-10) from the digits stored on its immediately adjacent and higher Difference, via the latter’s Upper Calculating Wheels. The Lower Calculating Wheels on this Axis are not ‘locked’ in this state, but free to move.

5. HALF-TURN: A 180 degree turn of the Vertical Adding/Calculating Axis and its Bolts. The Bolts have been locked or bolted in the previous turn to the Upper Calculating Wheels and will cause them to turn through the same angular distance as they themselves move until they are ‘unbolted’ by the Inner Inclined Planes fixed on the Lower Calculating Wheels in the same ‘Cage’. The angular orientation of these indicate the digit stored by that ‘Cage’. The angular displacement of this digit will therefore be transmitted to the Lower Calculating Wheel on the adjacent, next lower Difference to which the Upper Calculating Wheel is directly geared, and thence to the Figure Wheel on that Difference. After it has been ‘unbolted’ the Bolt will continue to rotate during this phase, free of the Upper Calculating Wheel until it is in its starting position front to back with the Engine again. A modulo-10 addition has been performed. During this phase the Lower Calculating Wheels on this Axis have remained ‘locked’ tight, so that the Bolts do not push them round as well when they encounter the Inner Inclined Planes.

6. lock: The Cams on the Vertical Bolting and Locking Axis come into action and lock the Lower Calculating Wheels on that Difference rigidly. Locking takes place for all ‘cages’ at the same time and commences when Bolting is complete. The Cams act throughout the next half-turn of the Bolting Axes, by which time the Bolting Fingers set around the other half of the shaft are restored to their starting position.

7. unlock: The Cams cease to act on the ends of their Levers and the Lower Calculating Wheels on that Difference are once again free to move.

8. The 6th Difference shows the action of Carrying in parentheses, thus (CARRY). This is because, although its Vertical Carrying (and Figure Wheel) Axis has Fingers, in normal Difference calculations the digits it carries remain constant and these Fingers therefore do not act on anything. If an Oblique Axis was connected to the 6th Difference and transfers of values from a lower Difference made via this Oblique Axis then Carriage of Tens might be carried out on it. Similarly the Table or Result Axis shows no action for Bolting. This is because it does not have a Bolting Axis, has no Bolts and no Upper Calculating Wheels which to bolt to. Neither does it perform the operation of Half-Turn but simply Add and Carrying, as shown. It does have a Locking Axis [see 20-Axis Mechanisms].

CALCULATING PART: BARRELS

The purpose of the Barrels in DE1 is to control the placing in and out of gear, at the appropriate times and in a fixed sequence, of the Vertical Carrying, Bolting and Adding/Calculating Axes, [and also, when the Engine is set to perform feedback operations by “eating its own tail”, the Intermediate Axes]. In this sense the Barrels carry the “program” for the calculation being undertaken by the Difference Engine. This “program” is set by the Mathematical Superintendent at the start of any table to be produced.

Each Barrel is a 5 inch diameter gun metal drum. The placing in gear of the various Vertical Axes is effected by means of Studs screwed to the curved surfaces of the Barrels. Each has 48 such fixing positions for Studs equally spaced around its circumference. Each acts on a sprung Roller Lever, the Roller of which runs around the surface of the drum as it rotates. When it encounters a Stud the other end of the Lever, which is connected with a Pin Clutch at the bottom of one of the Vertical Axes puts that Axis out of gear with its Mitre Wheel. If a blank position on the drum’s surface is met that particular Vertical Axis is put in gear with its mitre wheel ready to be driven. In a way this process is similar to the control mechanism found in a bell-tower carillon, in which a set of levers act on the studs of a rotating drum. These pull on a set of ropes attached to the bells causing them to be played in a fixed sequence. This results in a tune which can be repeated over and over again*.

Across the front side of the Engine and fitted just above the General Platform of the Engine is found the Carrying and Intermediate Barrel Axis. This carries 14 Barrels of the type described above, on which 14 Roller Levers act (7 for the Carrying (or Figure Wheel Axes) and 7 for the Intermediate Axes). This controls the timing for the process of the carriage of tens [and also the feedback operations via the Intermediate Axes and Oblique Axes, if the Engine is “eating its own tail”]. Connected to it by means a set of Mitre Wheels and a Communicating Axis on the backside of the Engine is found the Bolting and Adding Barrel Axis. This latter carries 12 Barrels of the above type and is responsible for the timing of the placing in and out of gear of the 6 Vertical Bolting and Locking Axes and 6 Adding/Calculating Axes. Again 12 Roller Levers (one for each Vertical Axis) act on these. Because of the interconnections both Barrel Axes and their Barrels rotate in unison.

The Mitre Wheel connected to the Carrying and Intermediate Barrel Axis and which drives the Mitre Wheel on one end of the Communicating Axis carries a dial or Notice Wheel to indicate the general orientation of the Barrels to the operator of the Difference Engine.

In normal difference calculations the Barrel Axes and the Barrels fixed on them are set to move forward twice during every Calculation Cycle of 4 Turns of the First Axis, alternately placing the odd and even vertical axes in and out of gear. When they move they do so by one 48th of a full turn (or 7.5 degrees or 1 Stud position.) It is so arranged that this takes place during the last 10th of a turn of the First Axis during the 1st and 3rd turns of the Calculating Cycle [3rd and 5th turns of the Short Result Cycle, or 7th and 9th turns of the Long Result Cycle].

To effect this 4 large wheels (ca 11.5″ in diam.) of 48 teeth fixed on two (intermediary) Axes lead the power from the First Axis or source of motion to a 5th 48-(toothed)-Wheel which drives the Carrying and Intermediate Barrel Axis (which in turn via the Communicating Axis drives the Bolting and Adding Barrel Axis at the back of the Engine). The First Axis drives the 1st 48-Wheel and its [intermediary] Axis by means of a wheel with a single tooth on it known as the 1st 48-Wheel Starting Tooth. For every turn of the First Axis this drives the 1st 48-Wheel a 48th of a revolution which in turn drives the 1st 48 (intermediary) Axis and a 2nd 48-Wheel fixed on it. The 2nd 48-Wheel then drives a 3rd 48-Wheel and its (intermediary) Axis which drives a 4th 48-Wheel fixed on it. This latter is in gear with the 5th 48-Wheel fixed on the Carrying and Intermediate Barrel Axis. The driving Wheels in this arrangement have square teeth, and each tooth on the driven Wheels is half-square and half-saw. The intermediary Axes are supported by brackets and plumbing blocks bolted to the underside of the General Platform of the Engine. The Axes run horizonatally to the long axis of the Engine under its Calculating Part.

This arrangement would drive the Barrel Axes forward one 48th every turn of the First Axis; such an arrangement could be made to work by a suitable pattern of Studs on the Barrels, but is not the one Babbage adopted in BAB.[U11]. The 2nd and 4th 48-Wheels have 48 removable teeth. In BAB.[U11] it seems that every second tooth on has been left off the 2nd 48-Wheel and the first in every group of three left off the 4th 48-Wheel. When the 2nd 48-Wheel is turned it only bites the 3rd 48-Wheel on every other turn of the First Axis, and when the 4th 48-Wheel is turned it only drives the 5th 48-Wheel and the Barrel Axes on the required turns. This arrangement gives the desired pattern of movement to the Barrels during the Short Result Cycles and the latter half of the Long Result Cycle (fifth to tenth Turns of the Cycle).

The Starting Tooth on the First Axis is connected to a Lever which acts on a Stud Wheel controlled by the 20-Axis. It is so arranged by horizontally sliding along the First Axis to come into gear with the 1st 48-Wheel when dictated by the Studs on the 20-Axis Stud Wheel on the 2nd tenth of a turn of the First Axis. BAB.[U11] shows this potentially happening on every turn of the First Axis (a dashed line at these times); i.e. the Starting Tooth for the arrangement shown on the chart remains in an active position to interact with the 1st 48-Wheel for all cycles, but that should it be required it can be put in or out of gear by the 20-Wheel Stud Wheel at these times.

The 1st 48-Wheel (intermediary) Axis can be driven by the First Axis by another means. There is a Pinion on the First Axis which has 30 teeth. This can interlock with the teeth of Sector Wheels fixed on the 1st 48-Wheel (intermediary) Axis. These latter Sector Wheels also have removable teeth which can be set to be from 0 to 144 in number. When this happens the First 48-Wheel Axis will be driven forward at a faster rate than that provided for by the Starting Tooth: 4.8 turns of the First Axis as compared with 48. BAB.[U11] shows this potentially happening [by dashed lines on the chart] during the first four turns of the Long Result Cycle. Babbage has, however, left no description of the purpose of this arrangement and we can therefore only speculate on this.

This speculation is made more difficult by the fact that I believe Babbage has made an error on BAB.[U11]. Each Line Cycle for a table of Logarithms, three Result Cycles for which I believe is what BAB.[U11] is trying to depict, is 64 turns of First Axis long: one Long Result Cycle of 10 turns and nine Short Result Cycles of 6 turns each. Whilst the arrangement of the teeth on the 2nd and 4th 48-Wheels described above is fine for the Short Result Cycles, during the Long Result Cycle the 4th 48-Wheel will get out of step, the length of the Long Result Cycle not being divisible by 3. It might be supposed that the Pinion and Sectors can be arranged to fast forward the 48-wheels and Axes over this problem during this particular Result Cycle bringing the arrangement back into step before the Short Result Cycles begin. This it cannot do as the Line Cycle is too long with respect to the number 48, the number of steps required to make a full revolution of the 1st 48-Wheel Axis and the Sectors fixed on it. The Sectors would be brought into action again for a second time long before the line was finished, which having brought the 4th 48-Wheel into step earlier would take it out of step again.

For DE1 to work in printing a table of Logarithms, a different arrangement from that described above is required: the 2nd 48-Wheel would again have every 2nd tooth missing and the 4th 48-Wheel would have the first in every group of three taken out of action. The Stud Wheel on the 20-Axis controlling the Starting Tooth of the 1st 48-Wheel would have its Studs so arranged as to take the Starting Tooth out of action during the first four turns of the Long Result Cycle, but putting it into gear for the last six turns and for all the Short Result Cycles. The Pinion and Sectors arrangement would be totally disabled, not being required.

The Barrels would be moved by this arrangement, as required, on every 3rd and 5th Turns of the Short Result Cycles and the 7th and 9th Turns of the Long Result Cycles. Their studs would be arranged in 24 adjacent pairs of equal patterns around the circumference, each pair of patterns putting the odd and even difference Vertical Axes in and out of gear alternately. The fact that the Barrels are not in step with the Line Cycle is irrelevant. During one Line Cycle the Barrels would rotate through 40 out of 48 steps; after 6 lines they would be back once again in step with the Line Cycles.

The arrangement described is for normal difference calculations. Different patterns of teeth on the 2nd and 4th 48-Wheels can be set, and, of course, many different arrangements of Studs on the Barrels are possible. For instance it would be possible to set it so that the 3rd Difference Axis could add its value to the 2nd Difference Axis 2 or 3 (or n, n being a whole number) times for every once the 2nd Difference Axis adds its value to the 1st Difference Axis. This flexibility gives DE1 the power to perform many different types of difference calculation other than the standard. In addition feedback calculations are possible by arranging for the Intermediate Axes to come into gear with the Figure Wheel Axes and by means of Oblique Axes transfer results from one set of Axes to others. The formulae for some of these are suggested in the paper by Lardner on DE1 (1834) [see footnote on P.73 Babbage’s Calculating Engines].

Driven by the 3rd 48-Wheel (intermediary) Axis is a 6th 48-Wheel which too has 48 removable teeth. [The Origin of Motion Chart on BAB.[U11] actually shows this wheel being driven by the 5th 48-Wheel, but the Timing Diagram beneath it indicates that its source of motion must be otherwise and as I suggest.] This wheel drives a 7th 48-Wheel which carries a Stud Wheel with 24 positions for Studs. These Studs are responsible for the timing at which the Starting Teeth of the 1st and 2nd 20-Wheels are slid horizontally on the First Axis into or out of gear with the Wheels they drive. Presumably the pattern of teeth on the 6th 48-Wheel is set to be the same as that on the 4th 48-Wheel so that the 7th 48-Wheel and its Studs are moved in unison with the Barrels. As printing is forbidden during those turns of the Axis when the Engine is adding differences to the Table Axis or resolving carriages of tens on it, since the pattern of studs on the Barrels indicate the turns on which these operations are performed, and as no printing takes place if the 20-Axis is not moved, it might be thought that the 7th 48-Wheel Studs signal to the 20-Axis department the times when printing operations are not allowed. This is not the case. On BAB.[U11] the Starting Teeth of the 1st and 2nd 20-Wheels are shown being moved into gear by the studs on the 7th 48-Wheel every turn of the First Axis during the last 10th of a turn.

See 20-Axis department for further details.

Note: * Carillon (from Latin ‘Quadrilionem’): originally 4 bells in a row struck by hand-held hammers xylophone style, later meaning extended to cover same 4 bells or up to 5 octaves of bells arranged in a chromatic (12 tone) scale. The Dutch in the 12th/13th century AD perfected a means of striking these bells automatically. They set up large revolving barrels several feet in diameter driven by water power or falling weights and a pulley mechanism. Around the circumference or surface of the revolving barrel or cylinder were set a series of pegs or pins (similar to those found in the later developed music boxes) which as the barrel turned would catch hold of a hammer or lever and release it to strike a bell. If the arrangement of pegs or pins was in the right order and the bells were caused to be struck at the right time intervals a tune would result. A different arrangement of pegs/pins would, of course, play a different melody. These tunes/melodies would be endlessly repeated as the barrels turned.

Calculating Part: Indicating Apparatus or Alarm Bells

This is sometimes called in the surviving Mss on DE1 ‘Apparatus for Pointing Out the Nines’ or any other figures come to that. It comprises:

a) Indicating Wheels A wheel of this type is fitted to the socket at the base of the Drum of every Figure Wheel, where it is retained by stiff friction. It can be turned by hand to any orientation so as to be able to point out any particular digit (0 to 9) that that Figure Wheel might arrive at. A line inscribed on its circumference assists in aligning it with the Index or Pointer on the Shade or Blind fixed to the framing, which points out the digit currently held by the Figure Wheel. The Indicating Wheel has a recess cut out of its circumference for the purpose of allowing an Indicating Roller to fall into it.

b) Indicating or Alarm Arms and Alarm Axes These are arms which are fitted to an axis one above the other, each projecting perpendicularly from a hollow, cylindrical Boss or Spindle loose on the shaft of the axis. Each Boss has a small slit in its side which receives a screw with a capstan head, which fixes it to the Axis so as to allow the Boss to slide up and down on the head of the screw, but to prevent the Boss from turning on the Axis. The axes are called Alarm Axes: there is one for each Difference. These Axes pass vertically through the Framing Plates behind the pillars which support the framing plates on the front side of the Engine, on the opposite side of the column of ‘Cages’ to the Carrying apparati. At the extreme end of each Arm is a notch made to receive a Roller (made of ivory?) which is retained on its arm by means of another small screw with a capstan head.

At the top of each Alarm Axis is an arm (fitted to the upperside of the top Framing Plate in the 1832 Fragment of DE1) which has and is acted upon by a Lever and Spring. This Spring presses all the Arms and their Rollers against the Indicating Wheels on that Axis. When all the Rollers drop into the notches in the Indicating Wheels (in an orientation when they are all directly behind the Figure Wheels when one is facing the Engine from its front side) then the hollow, cylindrical Bosses of the Arms all slip down on the head of the small screw which fixes them to the Alarm Axis; and when this happens, the topmost Arm or Lever lets loose a detent which pulls a wire attached to a Hammer, which, in turn, strikes a Bell. The purpose has been achieved: the Bell for that Difference is rung when all its Figure Wheels on that column reach the number which had been previously set by hand or ‘indicated’ by its Indicating Wheels. It is probable that Babbage intended the Bell on each Difference to have had a different tone, so that the Superintendent or Operator could know which Axis had rung and had thereby reached the desired number.

If all the Indicating Wheels on a particular Difference are set to indicate 9999 … 99, then when all the Figure Wheels on that axis reach that number, its bell will ring -indicating that ‘overflow’ is about to take place and all the wheels are about to pass through to 0000 … 00 (Zero or DE1’s Infinity). Babbage had hoped this could be used for two important purposes:

(1) to solve equations by finding their roots using the Newton-Raphson method.

(2) to prevent the Engine from calculating beyond its range of digits. It is probable that a mechanism would have been included which let loose a lever when a bell rang putting the calculating part of DE1 out of gear, and stopped it continuing.

This apparatus suffers from two major defects in its operation and thus fails in its principal purpose. It only correctly tests for a number if the Figure Wheels have completed a calculation and are still. Bromley (1986) has shewn that the Alarm mechanism would only have worked if the indicated number appeared on the column of Figure Wheels immediately after the process of Carrying. But if the column of Figure Wheels passed through this number during Carrying then the Indicating Arms would miss it, and Bell not ring when it might be expected to have. More than that the Alarm Bell would go off when not required to; that is after an Add process but before the Carriage of Tens; if the desired number was arrived at then the bell would ring, but, of course, the full process of addition has not been not completed, and the Engine has given us a false warning. It appears Babbage was ignorant of these defects.

Locking Mechanisms

Many of the parts in DE1 have been fitted with a Locking mechanism. Most of these consist of a wheel or cam with a scallopped edge around which the Roller of a sprung Roller Lever runs. The number of scallops on this wheel determines the number of ‘locking’ positions for the part concerned. This wheel is called a Locking or Roller Wheel.

There are two types of Locking:

(A) Rigid Locking. This involves the Roller of the Sprung Roller Lever being pressed solidly into one of the recesses in the scallopped edge of the Locking Wheel. In this instance the Roller Lever is often ‘double-ended’. Rigid Locking is effected by means of a Locking Cam or stud acting on the opposite end of the Roller Lever from its Roller. This locks the part to which the wheel is connected tightly in the given position until the Cam or stud is moved and the Roller released.

(B) Loose Locking. In this case the Roller of the Roller Lever is not pressed hard against its Locking Wheel, but is only held there lightly by the spring on the Lever. Levers of this type are usually only single-ended. Movement of the part to which the Locking Wheel is connected is allowed, but only in discrete steps determined by the positions of the recesses along the edge of the Locking Wheel. This effectively digitises the movement of the part concerned.

It is possible from the various manuscripts that have survived to identify most of those parts in DE1 which were supposed to have had a locking mechanism. A list of these follows. It is not necessarily complete, but as Babbage never left any overall account of them the existence of others can only be speculated upon. Itemized below are each of those parts known so far as having one, together with a description of its nature, the number of locking positions and any other relevant notes:

Great Wheel: Type B, 2 positions.

Horizontal Bolting Axis: Type B, 2 positions.

Horizontal Calculating Axis: Type B, 2 positions.

Horizontal Carrying Axis: Type B, 1 position.

Lower Calculating Wheels on 1st to 6th Differences: Types A and B, 20 positions. Type A locking occurs when the Locking Cams on the Vertical Bolting Axes act on the ends of the double-ended Roller Levers (see Bolting and Locking); Type B happens when the active edges of these Cams are pointing away from the ends of the Levers. The Lower Calculating Wheels each have 20 D-shaped upward-pointing crown teeth. These provide the necessary scallopping effectively making each its own Locking Wheel.

Lower Calculating Wheels and Snails on Table or Result Axis: Types A and B, 20 positions. The same as for the Lower Calculating Wheels on the other Differences, but in this instance the Locking Cams are found not on a Bolting Axis but are found instead on an Axis placed in the same position had the Table Axis had one. This Axis is called the Locking or Eccentrics Axis and is moved and controlled by the Lower 20-Axis and not by the Horizontal Bolting Axis. Type A locking occurs when the Locking Cams on the Vertical Eccentrics or Locking Axis act on the ends of the double-ended Roller Levers (see Bolting and Locking); Type B occurs when the active edges of these Cams point away from the ends of the Levers. The Lower Calculating and Snail Wheels of the Table Axis also each have 20 D-shaped upward pointing crown teeth. These again provide the necessary scallopping making each its own Locking Wheel.

Barrels: Type B, 48 positions.

20-Axis and 1st 20-Wheel: Type A, 20 positions.

2nd 20-Wheel: Type A, 20 positions.

Vertical Bolting/Locking Axes: each Type A, 2 positions. Their locking is not provided for by Roller Wheels but by the Pin Clutches. Each of these has two studs in the upper half of their mechanism. They work in this fashion: when the Bent Lever acts on a stud on the relevant Barrel (see Calculating Part:Barrels) these two studs lock rigidly the Vertical Axis concerned to two recesses in the Upper Platform (a gun metal plate fixed ca. 7 inches above the General Platform of the Engine).

Vertical Carrying Axes: each Type B, 1 position. Unlike the other vertical axes in the calculating part of DE1 Locking Wheels with sprung Roller Levers are fitted to the base of each Vertical Carrying Axis to provide for their locking.

1st 60-Wheel and Axis: Type B, 60 positions.

Calculating Part: On the Intermediate and Oblique Axes

In Bromley’s long review of Franksen’s article in the Annals of the History of Computing October 1983 Vol. 5 No.4 pp 411-415, he states on page 412:

“In section 12 Franksen deals with Babbage’s observation that the second difference of the sine function is itself proportional to the sine. He illustrates an implementation of this function within the conceptual framework of the Difference Engine. Babbage did provide facilities in the fragment of the Difference Engine [1833] whereby the engine could ‘eat its own tail’ by feeding back a digit of the tabulated function to the second difference, as alluded to in the note at the end of this review. The sine function could not be so generated, however, for there was no mechanism to effect the multiplication required. Collier has shown the critical importance of this example in the evolution of the Analytical Engine. To perform a multiplication requires the addition of many partial products; the ‘anticipating carriage’ was devised to speed these additions. The mechanical complexity of the anticipating carriage led, in turn, to the clear separation of the ‘mill’ (equivalent to the central processing unit of a modern computer) from the ‘store’, the axes of which relinquished to the mill all of the calculating power possessed by the axes of the Difference Engine.”

There is a need to clarify the points he has made about DE1’s power to produce a table of sines, and how Babbage intended to do it with special facilities he planned to incorporate in the machine. The key to understanding this was that the angles were to be measured in Radians, not Degrees. Babbage thought that DE1 did not need the full power of multiplication whilst ‘eating its own tail’ to do this, but hoped to have been able to produce the tables by a much simpler mechanism, the ‘stepping’ of powers of tens alone.

I quote with an extract from a letter from Babbage to JFW Herschel (Letter no.171, dated April 9th 1822. Herschel-Babbage Correspondence, Herschel Collection Vol 2: Royal Society, London):

“… Another idea concerning a table of sines to make by once setting an engine is not quite ripe but you shall have the embrio. You know that

D2sin Q = -(2.(sin h/2) 2 .sin(Q+h)) [See Below] suppose for a moment that in the difference of any two arcs in the table is such that

2.(sin h/2) 2 = .0001

then it would be easy to make a machine in which the second difference should be made by transferring the preceding tabular number cutting off the four figures at the end and such as one would make without interruption a table of Sin h, Sin 2h etc. …”

This is true as long as the arcs or angles are measured in radians. It was fortunate that Babbage got the principle right even though he had made a mistake in the above formula!

The correct formula for the above can be proved thus:-

Consecutive Values in a Table of Sines T-1 = Sin(x-h) (where x is the base value of the table T0 = Sin(x) and h its interval)

This is close enough to 0.01 to allow a Table of Sines interval 0.01 radians to be constructed using this method: viz. by making the second difference in the next calculation equal to the preceeding calculated value of the Sine function divided by 10,000 (ie. stepped down 4 decimal places). Babbage planned to achieve this by devising an apparatus which could be attached to the front of his DE1 which allowed it “to eat its own tail”.

[The following has been adapted with additions from CB’s own notes on the matter. Babbage’s Quarto Scribbling Book No. 12, Science Museum, London] That apparatus comprises of sets of special gun metal wheels, one for each figure wheel, on 7 vertical axes (6′ 4 3/4″ long 9/32″ diam.) parallel to each of the Figure Wheel Axes called “Intermediate Wheels and Axes”, (situated just to the left of each Figure Wheel Axis on the engine so as not to obscure the Figure Wheels themselves). Each of these Intermediate Wheels carries spur teeth which are always in gear with the immediately adjacent Figure Wheel. The upper side of each of these wheels carries a bevel wheel which gears with an inner bevel wheel on the cross studs. This gearing in made or broken for all the wheels at once by raising or lowering the Intermediate Axes. The latter is controlled by levers acting on the studs or the absence of studs on the Intermediate and Carrying Barrel.

The Intermediate Axes are supported by additional parts projecting from every fourth framing plate. Through the extremities of all these projecting plates pass two collar bolts, which bolts pass through four pairs of sockets each pair connected by a cross bar. In each of these cross bars is screwed a horizontal stud on which turns a double bevel wheel attached to an Intermediate Wheel, the other end of which gears with a bevel on the Oblique Connecting Axis [called ‘Oblique’ as they cross the front of the machine obliquely].

The Oblique Connecting Axes turn in collars which screw into the horizontal studs and at their other end have bevel wheels which connect them with a similar set of apparatus on another Difference Axis.

Depending on the setting of the machine, by and large even numbered axes could be connected either additively [but not subtractively, see below] in this fashion to other even numbered difference axes [Table, 2nd, 4th or 6th], or odd numbered axes to odd [1st, 3rd and 5th].

The formulae for the connection would not have been: Next value on 2nd Difference axis [or other even numbered axis] = value on Table axis/10,000 [or other power of 10] But rather Next value on 2nd Difference axis = Old value on 2nd Difference axis + (Value added to Table axis [from 1st difference axis]/10,000).

In fact two sets of steel oblique axes were made by Clement for DE1: [From accounts held in the Public Record Office, Kew] 4 short (6ft 6ins long 19 /32 ins diam.) and 4 long (7ft 6ins long 19 /32 ins diam.)

Given this apparatus, if it had worked (see below), and the above formulae it would have been a very easy matter for DE1 to have produced a Table of Sines in Radian Measure for intervals of 0.01 radians, 0.001 radians, 0.0001 radians etc.. It would also have been a very easy matter, in its normal mode, for the engine to have produced a Table converting Degrees to Radians. (It would not have been so easy for it to produce the reverse, Radians to Degrees, as Degrees do not lend themselves readily to the Decimal System so well. In any case Babbage, being a first and foremost a mathematician, would probably have preferred his Sine Tables to have been in Radians anyway.) Anyone possessing a programmable pocket scientific calculator with at least three memories can demonstrate for themselves the principle upon which it is based.

The fact is, however, the Oblique and Intermediate Axes apparatus would have worked in the production of Hyperbolic Sines as positive values of differences would have been added to one another. But as the production of a Table of Sines requires the subtraction of the 2nd Difference from the 1st, which could only be performed by DE1 by the adding of negative complements, the proposed apparatus would not have worked properly. It is probable Babbage was not aware of this defect: I am grateful to Allan Bromley for pointing out this fault in his reasoning.

PRINTING DEPARTMENT

20-Axis (or Printing Axis) Department

The 1st 20-Wheel and the 20-Axis. The 1st 20-Wheel is a 20 cog-toothed wheel fixed on a shaft called the 20-Axis parallel to the 1st Axis. It can be locked in 20 possible orientations. Its job is to count the number of digits in a result that have been stamped, and to select the next or to report that the punching of a result has been completed, and that it is time to calculate the next. The 20-Axis has two motions.

Digit by digit motion: for each turn of the handle, it is driven forward one position by a single tooth located on the 1st Axis. This latter is placed in gear with the 20-Wheel by a lever acting on a stud wheel in the Barrels Department. This tooth is oriented to act on the 2nd tenth of each turn of the First Axis.

Fast forward motion: this is required to wind the 20-Wheel mechanisms back to their starting position. On the 20-Axis are a pair of adjustable sector wheels, one fixed the other movable, which are driven by a pinion on the First Axis. 2 turns of the First Axis are allowed for fast forward motion, which is usually set to occur on the 5th and 6th turns of the First Axis in each result cycle of 6 turns. During the turn just before extended result cycles have to occur the movable sector is slid out of contact with the pinion on the First Axis. This allows the 4 most significant digits of a result to be selected and punched when they need to be.

The 1st 20-Wheel dept directly controls: (a) The orientation of the Spiral Axis hence selects digits to be punched on that turn. And the locking of the Calculating Wheel bearing the value being punched. (b) A Stud Wheel to put the Barrels Department in/out of gear. (c) The orientation of various Sine-Qua-Non Wheels Two which put the Returning and Zig-Zag Motion Cranks in/out of gear. And one which controls the timing of the swinging in/out of the Type Sector.

2nd 20-Wheel Department. On the 20-Axis, running loose around it, is another component called the 2nd 20-Wheel. This too has 20 cog-teeth and 20 possible orientations, and also its own locking mechanism. It too is driven forward by a single tooth on the First Axis. This tooth is set behind that which drives the 1st 20-Wheel, and is arranged to come into action on the 8th tenth of a turn of the First Axis. The 1st 20-Wheel dept acts on each turn of the First Axis before digits are punched, whereas the 2nd 20-Wheel dept deals with those actions required afterwards. Both single teeth are placed in/out of gear at the same time as they are controlled by the same stud wheel in the Barrels Department. This takes places on the 9th tenth of a turn of the First Axis.

The job of the 2nd 20-Wheel is to control (a) A stud wheel which determines the time when the Calculating Part comes into action. (b) The format and spacing of the punching of results by means of two stud wheels. (c) The timing of the engagement of the Friction Cones which pull the Copper Plate along to the next digit position.

When the 1st 20-Wheel is zeroed by means of fast forward motion so too is the 2nd 20-Wheel. There are a pair of arms to effect this.

Selection and Punching of Results

Punching. DE1 wants to punch a digit on each turn of the First Axis. For each turn the Forcer of the Punches bobs up and down once. This happens whether a punch is underneath it or not. If a punch is in position then the digit it bears will be stamped on the Copper Plate, otherwise the Forcer continues to act but without effect. The Forcer is driven by a cam turned by a direct train of shafts geared with the First Axis

The Spiral Axis. The 20-Axis described above drives the Lower 20-Axis parallel to it at the rear of the machine. This axis drives a Communicating Axis. This latter passes right underneath the machine driving the Spiral Axis on the front side of the Engine. The Spiral Axis is a vertical shaft around whose body are set, protuding in a spiral, 18 fingers and two blank positions, one for each digit on the Result Axis. Thus for each turn of the First Axis the Spiral Axis moves round one twentieth. As a conseqence of its physical arrangement one of its fingers ends up being closer to the Type Sector than the others. This is the finger that is opposite that digit on the Result Axis to be stamped on that particular turn.

Type Sector and Axis. The Type Sector is DE1’s daisy-wheel-like mechanism. It is a 45â frame for holding 11 vertical punches, one for each digit 0-9 and the decimal point. It swings around a vertical axis in a horizontal plane. On its vertical shaft are 18 arms set one above the other, one opposite each digit on the Result Axis. At the end of each is a Drop Pin which can click up and down like a retractable biro.

On the First Axis is a Cam which causes the Type Sector and its Axis to swing in underneath the Forcer and out again towards the Spiral Axis. This happens on each turn of the First Axis when a digit has to be punched. Otherwise a detent controlled by a SQN wheel holds it back out.

On the First Axis is yet another Cam. This lifts the Spiral Axis up and down once for each turn of the First Axis. That finger on the Spiral Axis which is closest to the Type Sector Axis’ arms when the latter swings out lifts that Drop Pin closest to it. All the remainder remain down. When the Type Sector Axis swings back in again this Drop Pin is up, whilst all the others are down. On swinging back out again the Spiral Axis pushes this Pin back down again when it is lowered by the Cam.

Selection of Value of the Digit to be punched. Fitted to each Lower Calculating Wheel on the Result Axis is a Snail Wheel. These are cam-like devices with two limbs, shaped rather like a double spiral galaxy. They have been specially designed to present a different radius for each value of the digits borne by the Lower Calculating Wheel. When the Type Sector Axis swings in, that Drop Pin which is up strikes against its corresponding Snail Wheel, causing the swinging to halt. Depending on the Snail Wheel’s orientation so the Type Sector adopts the appropriate angle corresponding to the value of the digit required to be punched.

Figure to Figure Motion of the Copper Plate

On the First Axis are two cranks. For each turn of the First Axis these pull ratchet wheels fixed to an axis at the rear of the Engine. The amount the Ratchet Axis is turned depends on the number of teeth that are exposed on the ratchet wheels. Each has a shade which covers or reveals a different number of its teeth. There are two stud wheels, one for each ratchet, on the 2nd 20-Wheel, which control the movement of the shades.

The Ratchet Axis drives the Endless Screw Wheel of the Figure to Figure Motion department. If two pairs of Cones have been pressed together then, by friction, the Endless Screw Wheel will turn the Ribbon Axis. This in turn drags the Copper Plate in its frame along the Upper Slider to the next figure stamping position. The timing of the pressing together of the Cones is controlled by a SQN Wheel on the 2nd 20-Wheel.

In turning the Ratchet Axis the Cranks act additively. In switching the ratchets’ shades on/off the Stud Wheels on the 2nd 20-Wheel determine the spacing of the digits in and between results. In this way DE1 can deal with different size typefaces.

The 60-Wheels Department

Its job is to count how many results have been calculated and punched, and then to determine certain actions after a particular number of these have taken place. It comprises 3 large wheels called respectively the 1st, 2nd and 3rd 60-Wheels set on a shaft called the 60-Wheel Axis. The 1st and 3rd 60-Wheels are fixed on the axis and rotate in unison together. The 2nd runs loose, but is driven by movable teeth on the 1st 60-Wheel. A locking mechanism holds the 1st 60-Wheel in place. The 2nd 60-Wheel has its own separate locking mechanism. Each of the wheels has 60 orientations. The number 60 was chosen as it has a large number of divisors suitable for specifying the number of columns in tables. For each turn of the 20-Axis, i.e. one result, a single tooth on the 20-Axis drives the 1st 60-Wheel forward one position.

The 1st 60-Wheel has two sets of studs. One set determines when the Returning Crank is to be placed in/out of gear: this identifies how many results across the page are to be stamped (2, 3, 5, 6, 10, 12 etc.). The other side determines when the Zig-Zag Motion Crank is to be placed in/out of gear. The 3rd 60-Wheel has 30 studs. These determine which of the result cycles are abbreviated ones and which are extended. Its studs place in/out of gear the movable portion of the Sector Wheel which fast forwards the 20-Axis.

The 2nd 60-Wheel counts the number of lines that have been punched. After a particular number of these it specifies when a wider line spacing is to be used. Its studs control the shade of the teeth on the Line to Line Motion Ratchet Wheel.

Cranks Department

These are DE1’s “carriage return line feed” mechanisms. They return the Copper Plate to the start of lines and move the frame down so that new lines of results can be punched. This action takes two turns of the First Axis.

Returning Motion and Zig-Zag Motion Cranks. A wheel on the First Axis drives another wheel and a shaft perpendicular to it. On the shaft is a spur wheels which drives two other wheels, one which drives the Returning Crank Clutch and the other the Zig-Zag Clutch. If the Clutches have been placed in gear, determined by levers acting on the studs on the 1st 60-Wheel, then at a time in the Result Cycle specified by the SQN wheels on the 20-Axis the First Axis will drive the Returning and Zig-Zag Motion Cranks. These two mechanisms work in opposite directions. The Returning Motion Crank pulls the Upper Slider on which the Copper Plate rides back to the start of lines. The Zig-Zag Crank pulls the frame forward along a line and is responsible for general column layout of tables.

Line to Line Motion Crank. At the same time that the Copper Plate is backed a wheel on the Returning Crank Axis drives the Line to Line Motion Axis. This drives a crank which pulls a ratchet wheel with a shade. This shade controls the number of teeth exposed on the Ratchet and is itself governed by the studs on the 2nd 60-Wheel. It determines when single or 1½ line spacing is to be used. Through a train of mechanism this drives an Endless Screw which pulls the Lower Slider giving Line to Line Motion to the Copper Plate.

3-Figure Motion Department

To save time, paper, size of table to be punched etc., about 30%, to make the tables produced by DE1 more readable Babbage devised a special formatting device which enabled his Engine to punch two different layouts for results:-

(a) Extended or Full Result (b) Normal or Abbreviated Result

Extended results were used when all the digits of a result were to be punched. Normal results were used when only the last n (n=4, say) least significant digits were to be stamped. Extended results were intended to occur at the beginning of each line of results, but only when the significant digits of a result had changed. Otherwise normal or abbreviated results were to be used. Babbage’s manually produced Logarithm Table (1826) illustrates this layout.

The timing of extended result cycles is determined by the 3rd 60-Wheel. At the beginning of each line the first result to be stamped always requires an extended result cycle (of say 10 turns of the first axis). Whether or not a full or abbreviated result is stamped, however, is decided by the 3-Figure Motion Department.

One of the Lower Calculating Wheels (say the 5th significant digit’s) is screwed to the Result Column’s Calculating Axis. All the others run loose around it. Note that there are no bolts on the Result Column and thus no conflict of interest occurs. At the base of the Calculating Axis are fixed a pair of arms. These arms adopt the orientation of the fixed Calculating Wheel. Whenever that Calculating Wheel passes over from 9 through to 0 one of these arms, via a series of levers, triggers the release of the 1st detent of the 3-Figure Motion Bar. This indicates that there has been a change in the value of say the 4th significant figure on the Result Axis. The 2nd detent of the 3-Figure Motion Bar is released by the Line to Line Crank at the end of a line of results. When the Bar is released this causes the movable part of the 3rd Sine-Qua-Non Wheel (part of the 1st 20-Wheel department) to be slid out of action. When both detents have been released this allows the first few significant figures of result to be stamped. Otherwise the Type Sector is held out of action are not permitted to swing in for punching during these first few digits. DE1 will go through the motions of attempting to punch a full result with all its digits at the beginning of the line, that is require the same number of turns of the first axis of an extended result cycle, but without effect, only stamping an abbreviated result.

Upon completion of its action the 3-Figure Motion Bar and its detents are reset by an inclined plane acting on the 3rd Sine-Qua-Non Wheel.

Selection and Punching of Results

(a) Punching

DE1 wants to punch a digit on each and every turn of the First Axis. For each turn of the First Axis the Forcer of the Punches bobs up and down once. This happens on every turn whether a punch is underneath the Forcer or not. If one of the punches from the Type Sector is in position underneath the Forcer then the digit it bears will be stamped on the Copper Plate. If not then the Forcer will still continue to perform its action but without effect.

On the First Axis is fixed a mitre/bevel wheel which drives another perpendicular to it fixed on a vertical shaft, called the Vertical Punching Axis. This connects in turn to a horizontal shaft, called the Horizontal Punching Axis, via yet another pair of mitre/bevel wheels. On the Horizontal Punching Axis is a cam which drives the top end of the Forcer down. It does this at the same time as controlling the timing of this action.

On the Vertical Punching Axis is another cam which operates a sprung roller lever which steadies the Type Sector during the Punching process.

(b) 1st 20-Wheel, 20-Axis, Excentrics Axis and Spiral Axis On the First Axis

1st 20-Wheel, 20-Axis, Excentrics Axis and Spiral Axis On the First Axis is a single tooth which drives a 20 cog toothed wheel called the 1st 20-Wheel round through one of its 20 orientations for each complete turn of the First Axis. The 20-Axis to which the 1st 20-Wheel is fixed via a pair of spur pinions drives the Lower 20-Axis parallel to it at the rear of the machine. This axis in turn drives a Communicating Axis via yet another pair of bevel wheels. The Communicating Axis passes right underneath the Machine at an oblique angle. This axis is directly connected via another pair of bevel wheels to the base of the Spiral Axis on the front side of the Engine and drives it. The Spiral Axis itself is a vertical shaft around whose body are set protuding in a spiral 18 fingers and two blank positions, one for each digit on the Result Axis. Thus for each turn of the First Axis the Spiral Axis moves round one twentieth of a turn.

As a conseqence of this motion and of the physical arrangement of the fingers on the Spiral Axis, one of the fingers on it ends up being closer to the Type Sector when it swings out. This is the finger that is opposite to the cage of the digit of the Result Axis to be stamped on that particular turn of the First Axis.

At the same time the Lower 20-Axis turns the Excentrics Axis through one of its 20 orientations. It has a spiral of 18 Locking Studs set around it shaft. One of the studs becomes active and locks the Lower Calculating Wheel (via a lever acting on the Ds of the Lower Calculating Wheel in a similar fashion to the locking action of the Vertical Bolting Axes). It, in particular, locks that one which carries the digit which is to be selected for punching on that turn of the First Axis.

A locking mechanism on the 20-Axis with 20-orientations holds all the above mechanism tight in position after moving. There is a lever on the First Axis which releases this locking mechanism when necessary.

The Type Sector is DE1’s daisy-wheel-like mechanism. It is a 45 degrees frame for holding 10 vertical punches, one for each digit. It swings around a vertical axis in a horizontal plane. On the vertical shaft of the the Type Sector Axis are 18 arms set in a vertical plane one above the other, one opposite each digit cage on the Result Axis. At the end of each arm is a Drop Pin which can click up and down like a retractable ball-point pen.

On the First Axis is a Cam which causes the Type Sector and its Axis to swing in underneath the Forcer of the Punches and out again towards the Spiral Axis. This happens once for each turn of the First Axis but only on those turns when a digit is to be punched. Otherwise a detent controlled by the 2nd SQN wheel holds it back out.

On the First Axis is yet another Cam. This lifts the Spiral Axis up and down once for each turn of the First Axis. The finger on the Spiral Axis which is closest to the Type Sector Axis’ arms when the latter swings out lifts that Drop Pin on the arm closest to it up. All the remainder remain down. When it swings back in again the Type Sector this Drop Pin is up, whilst all the others are down. On swinging back out again the Spiral Axis pushes this Pin back down again when it is lowered by the Cam.